area and perimeter problem solving

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Area and Perimeter of Rectangle

Welcome to our Area and Perimeter of Rectangle worksheets and support page. Here you will find a range of free printable worksheets which will help your child to learn to work out the areas and perimeters of a range of rectangles and rectilinear shapes.

These sheets are aimed at children from 3rd to 5th grade.

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Area and Perimeter of Rectangle Support

On this webpage you will find our range of worksheets to help your child learn to work out the area of a range of rectangles.

These sheets are graded from easiest to hardest, and each sheet comes complete with answers.

Using these sheets will help your child to:

• understand what area and perimeter are;
• know how to find the area and perimeter of a rectangle;
• find areas and perimeters involving fractions;
• solve word problems and challenges involving areas and perimeters of rectangles.

Want to test yourself to see how well you have understood this skill?.

• Try our NEW quick quiz at the bottom of this page.

Quicklinks to ...

What is Area?

What is perimeter.

• Area & Perimeter of a Rectangle Worksheets
• Area & Perimeter of a Rectangle Challenges
• Area & Perimeter of a Rectangle Word Problems
• Area & Perimeter of Rectilinear Shapes Worksheets
• More recommended resources

Area & Perimeter of a Rectangle Online Quiz

• Area is the amount of space that is inside a shape.
• Because it is an amount of space, it has to be measured in squares.
• If the shape is measured in cm, then the area would be measured in square cm or cm 2

Area of a Rectangle

• If you are measuring the area of a rectangle, then the area will equal the length multiplied by the width.
• Or Area of a rectangle = length x width.
• The area of the rectangle below is 5 x 3 = 15 squares.
• Perimeter is the distance around the outside of a shape.
• It can be measured in cm, inches, feet, yards, km, miles, etc.

A good way of thinking about the perimeter of a shape in front of you is to imagine that you are very small and standing on one of the corners of the shape. Imagine walking along the sides of the shape until you get back to where you started. The distance you have walked will be the perimeter.

For more help with perimeter please use: this link.

How to find the perimeter of a rectangle

To find the perimeter of a rectangle, there are several different ways, you can use the one you prefer:

• Add up the lengths of each side seperately
• Double the lengths of the adjacent sides and add them together.
• Add the adjacent sides and double the answer.

Perimeter Example

Find the perimeter of the rectangle below.

We will work the perimeter out using the 3 different ways above:

• Add up the lengths of each side separately: 7 + 2 + 7 + 2 = 18
• Double the lengths of the adjacent sides and add them: double 7 + double 2 = 14 + 4 = 18
• Add the adjacent sides and double the answer: double (7 + 2) = double 9 = 18

Area and Perimeter Worksheets

Area and perimeter sheets 3rd grade.

• Area and Perimeter of Rectangles Sheet 1
• PDF version
• Area and Perimeter of Rectangles Sheet 2

Area and Perimeter Sheets 4th Grade

• Area and Perimeter of Rectangles Sheet 3
• Area and Perimeter of Rectangles Sheet 4

Area and Perimeter Challenges

The aim of these challenges is to get children to apply their knowledge of area and perimeter to solve problems and look for patterns in their results.

• Area and Perimeter of Rectangles Challenge 1
• Area and Perimeter of Rectangles Challenge 2
• Area and Perimeter of Rectangles Challenge 3

Area and Perimeter Problem Solving

Each problem needs to be identified as either an area problem or a perimeter problem and then solved..

The problems on the sheet are identical, but the measurements get progressively harder to do!

These sheets are designed for kids from 3rd to 5th grade.

• Area and Perimeter Word Problems Sheet 1A
• Area and Perimeter Word Problems Sheet 1B
• Area and Perimeter Word Problems Sheet 1C

Area and Perimeter of Rectilinear Shapes

These sheets involve working out the area of rectilinear shapes.

A rectilinear shape is a shape made out of rectangles.

Find the perimeter by adding up the side lengths (you many need to work some of them out first!)

Find the area by working out the areas of the rectangles and adding them up!

These sheets are suitable for 4th and 5th graders.

There is a support video to help you solve these problems underneath the sheets.

• Area and Perimeter of Rectilinear Shapes 1
• Area and Perimeter of Rectilinear Shapes 2

Area and Perimeter of Rectilinear Shapes Walkthrough Video

This short video walkthrough shows our Area and Perimeter of Rectilininear Shapes Worksheet 1 being solved and has been produced by the West Explains Best math channel.

If you would like some support in solving the problems on these sheets, check out the video!

More Recommended Math Worksheets

Take a look at some more of our worksheets similar to these.

• Rectangle Area and Perimeter Calculator

Our handy area and perimeter calculator will find the area and perimeter of a range of rectangles.

The best feature is that it shows you all the working out, step-by-step.

More Area Worksheets

This section contains worksheets on area at a 5th and 6th grade level.

The focus is on calculating the area of triangles and different quadrilaterals.

• know how to calculate the area of a triangle;
• know how to calculate the area of a range of quadrilaterals.
• learn the formulas to calculate the area of triangles and some quadrilaterals.
• Area of Rectangle Worksheets (area only)
• Area of Right Triangle
• Area of Equilateral Triangle
• Area of Parallelogram Worksheets
• Area of Quadrilaterals Worksheets
• Perimeter Worksheets

Here is our selection of free printable perimeter worksheets for 3rd and 4th grade.

The sheets are all graded in order from easiest to hardest.

• work out the perimeter of a range of rectangles;
• find the perimeter of rectilinear shapes.

All the sheets in this section support Elementary Math Benchmarks.

• What does perimeter mean? Support page

Our quizzes have been created using Google Forms.

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For incorrect responses, we have added some helpful learning points to explain which answer was correct and why.

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We would be grateful for any feedback on our quizzes, please let us know using our Contact Us link, or use the Facebook Comments form at the bottom of the page.

This quick quiz tests your knowledge and skill at finding the area and perimeter of a rectangle here. It is aimed at 3rd and 4th graders.

Fun Quiz Facts

• This quiz was attempted 1,182 times in the last academic year. The average (mean) score was 15.3 out of 22 marks.
• Can you beat the mean score?

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60 Fun Area and Perimeter Word Problems | Free Worksheets

These area and perimeter word problems worksheets will help to visualize and understand area and perimeter. 3rd to 5th-grade students will learn the basic techniques to solve area and perimeter related word problems and can improve their basic math skills with our free printable area and perimeter word problems worksheets.

5 Exciting Worksheets for Practicing Area and Perimeter Word Problems

Please download the following word problem worksheets and find area and perimeter on the pages.

Triangle Problems

Quadrilateral Problems

Circle Problems

Real-Life Problems

Polygon Problems

Introduction to Area and Perimeter

Let’s learn some basics about area and perimeter. In simple words, the area is the whole amount of space inside an object. For example, for the rectangle shown in the following image, the region inside the square shape is its area.

Whereas perimeter is the measured distance around a shape. The following image will give you a better understanding. 

It’s a common thing to find the area and perimeter of various shapes. Generally, we calculate these terms for triangular and quadrilateral shapes. But you can also find area and perimeter for other shapes as well.

Triangle Area and Perimeter Word Problems

A space surrounded by three sides is called a triangle. A triangle has three sides and three angles. How can we find the area and perimeter of a triangle?

Follow the below given image below for a better understanding.

If you have understood the above concept, then practice the relevant exercises given in the worksheets.

Quadrilateral Area and Perimeter Word Problems

Quadrilaterals are geometrical shapes that have four sides and four angles. Square, rectangle, parallelogram, rhombus, trapezium, etc. are some of the most known and used quadrilaterals.

The following word problems will help you enhance your skill in finding the area and perimeter of various quadrilaterals.

Circle Area and Circumference Word Problems

Another familiar geometrical shape that we see every day is a circle. For a circle, we can also find its area and circumference. We will use the term circumference instead of the perimeter for a circle. Like a perimeter, a circumference is a line that runs around or encircles a circle.

Mainly, it is the outer boundary of a circle. See the following image to get a better understanding of the area and circumference of a circle.

Real-Life Area and Perimeter Word Problems

In this section, you will solve some real-life area and perimeter word problems. How are the above shapes related to our real lives, and how can we use tactics to find areas and perimeters for these real-world shapes? We will find out the answers to the above questions in the following worksheets.

Polygon Area and Perimeter Word Problems

Finally, we are going to solve some perimeter word problems for regular polygons. Here, we will take polygon shapes that have more than four sides. We will find only the perimeters of these shapes.

How we will do that, is explained in the following image.

Also, if the polygon is not regularly shaped, then you have to add all the sides of that irregular polygon to get its perimeter. Like we did in the following image.

Area and Perimeter Word Problems Challenge

A rectangular floor has dimensions of 10 feet by 12 feet. You want to cover the floor with square tiles that are 1 foot by 1 foot. What is the total number of tiles you need to cover the floor, and what is the perimeter of the tiled floor?

Solution: First, let’s calculate the area of the rectangular floor:

Area of floor = length x width = 10 feet x 12 feet = 120 square feet

Since each tile is 1 foot by 1 foot, the area of one tile is 1 square foot. To find the number of tiles

needed to cover the floor, we can simply divide the area of the floor by the area of one tile:

Number of tiles = area of floor / area of one tile

Number of tiles = 120 square feet / 1 square foot per tile

Number of tiles = 120 tiles

So you’ll need a total of 120 square tiles to cover the entire floor.

Next, let’s calculate the perimeter of the tiled floor. Since the tiles are each 1 foot by 1 foot, the

perimeter of the tiled floor will be the same as the perimeter of the rectangular floor. The

perimeter of a rectangle is found by adding the lengths of all four sides. So:

Perimeter of floor = 2(length + width)

Perimeter of floor = 2(10 feet + 12 feet)

Perimeter of floor = 2(22 feet)

Perimeter of floor = 44 feet

Therefore, the perimeter of the tiled floor is 44 feet.

Download Free Printable Worksheet PDF

Download the following combined PDF and enjoy your practice session.

So today, we’ve discussed area and perimeter word problems worksheets using the concepts of area and perimeter of various geometrical shapes induced with some interactive word problems. Download our free worksheets, and after practicing these worksheets, students will surely improve their mathematical skills and have a better understanding of area and perimeter related word probelms.

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Area and Perimeter

The area of a shape is the space inside the shape. Area is measured in squares.

Finding the area of a rectangle

Here is a rectangle drawn on a centimetre grid.

To find the area of a rectangle multiply the length by the width. (We could also count the squares but this will not work from more complex questions)

In this example we have a length of 6cm and a width of 3cm.

Area = length × width Area = 6 × 3 Area = 18 cm 2

The units are cm 2 : one cm 2 is a square that measures 1cm by 1 cm.

Example 1: A rectangle is drawn on a centimetre grid Calculate the area of the rectangle

Area = length × width Area = 5 × 4 Area = 20cm 2

A rectangle is drawn on a centimetre grid. Calculate the area of the rectangle.

Finding the area of a triangle

We can think of a triangle as half of a rectangle

To calculate the area of a triangle we can half the area of a triangle

The area of a triangle = 1 ⁄ 2 × base × height

Example 2: Here is a triangle drawn on a centimetre grid. Calculate the area of the triangle.

Area = 1 ⁄ 2 × base × height Area = 1 ⁄ 2 × 4 × 6 Area = 2 × 6 Area = 12cm 2

Example 3: Calculate the area of the triangle.

For the area calculation we use the perpendicular height (it must be straight up, not diagonal). The height of this triangle is 12 metres.

Area = 1 ⁄ 2 × base × height Area = 1 ⁄ 2 × 8 × 12 Area = 4 × 12 Area = 48m 2

A triangle is drawn on a centimetre grid. Calculate the area of the triangle.

Calculate the area of the triangle.

Finding the area of a parallelogram

A parallelogram is a quadrilateral with two sets of parallel sides.

A parallelogram can be made into a rectangle by cutting off and moving a triangle:

The area of a parallelogram = base × height

Example 4: Here is a parallelogram drawn on a centimetre grid. Calculate the area of the parallelogram.

Area = base × height Area = 4 × 3 Area = 12cm 2

Example 5: Calculate the area of the parallelogram.

For the area calculation we use the perpendicular height (it must be straight up, not diagonal). The height of this parallelogram is 11 metres.

Area = base × height Area = 8 × 11 Area = 88m 2

A parallelogram is drawn on a centimetre grid. Calculate the area of the parallelogram.

Calculate the area of the parallelogram.

Finding the area of a trapezium

The image below shows a trapezium, a trapezium (trapezoid in American English) is a quadrilateral with two parallel sides.

The area of a trapezium = 1 ⁄ 2 (a + b) × height Where a and b are the lengths of the two parallel sides

This formula can be made by splitting the trapezium into a rectangle and a triangle (you don't have to know where the formula comes from, you just have to know the formula).

Example 6: Find the area of the trapezium

For the trapezium above: Area = 1 ⁄ 2 (6 + 10) × 7 Area = 1 ⁄ 2 (16) × 7 Area = 8 × 7 Area = 56 cm 2

A trapezium is drawn on a centimetre grid. Calculate the area of the trapezium.

Calculate the area of the trapezium.

The perimeter of a shape is the distance around the edge of the shape

To find the perimeter of a shape we add up the lengths of all of the sides

This rectangle has two sides with a length of 6cm and two sides with a length of 3cm

Perimeter = 6 + 6 + 3 + 3

Perimeter = 18 cm

Example 1: A rectangle is drawn on a centimetre grid Calculate the perimeter of the rectangle

Perimeter = 5 + 5 + 4 + 4 Perimeter = 18cm

Example 2: Calculate the perimeter of the triangle

Perimeter = 10 + 9 + 7 Perimeter = 26m

A rectangle is drawn on a centimetre grid. Calculate the perimeter of the rectangle.

Calculate the perimeter of the rectangle.

Area and perimeter problems: rectangles and rectangular shapes

This is a problem solving lesson in which we solve several problems involving both area and perimeter of rectangles or rectangular shapes. It is suited to grades 3-5.

The first problem involves a shape that we can divide into several rectangles, and then figure its area and perimeter. Some side lengths are missing — but we can find those by subtracting.

Then our task is to draw rectangles with an area of 20 square units. There are several, of course. I write in the table their side lengths, and then we also calculate the perimeter of each. We notice how the skinniest rectangle has the largest perimeter, and the rectangle that is closes to a square has the least perimeter (of these three)!

Our last problem is almost like a puzzle — draw a rectangle with an area of 60 square units and a perimeter of 34 units. Guess and check helps!

If you cannot see the video above, click here for an alternative video player.

Math Mammoth Early Geometry — a self-teaching worktext with explanations & exercises for beginning geometry topics (grades 1-3)

Math Mammoth Grade 3 complete curriculum

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Length and Area Problem Solving

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• A Former Brilliant Member

To solve problems on this page, you should be familiar with the following: Perimeter Area of Triangle Area of Rectangles Area of Circles

You should also know the following formulas:

• Square with side length \(L\): Area is \(L^2\), and perimeter is \(4L \).
• Rectangle with side length \(L\) and breadth \(B\): Area is \(L\times B\), and perimeter is \(2(L+B) \).
• Equilateral triangle with side length \(s\): Area is \( \frac {\sqrt3}4 s^2 \), and perimeter is \(3s\).

If the area of a square is 144, what is the perimeter of the square? ANSWER Let \(L\) denote the area of the square, then \(L^2 = 144 = 12^2 \) or \(L =12\). Note that we are only taking the positive root because \(L\) represents a physical dimension. Thus the perimeter of the square is \(4L = 4\times 12= 48. \ _\square\)

The ancients talked about "squaring the circle," by creating a square and a circle which have the same area. If the radius of the circle is 1, what would be the side length of the square? ANSWER Let the side length of the square be \( S \). Then, we are given that \( S^2 = \pi \times 1 ^2 = \pi \). Taking square roots, we obtain \( S = \sqrt{\pi } \). \(_\square\)

If the ratio of the area of a square to the area of an equilateral triangle is \( 4 : 3 \), what is the ratio of the side length of the square to the side length of the equilateral triangle? Let the side length of the square be \(S\). Then the area of the square is \(S^2 \). Let the side length of the equilateral triangle be \(T \). Then the area of the equilaterial triangle is \( \frac{ \sqrt{3}} {4} T^2 \). We are given that \( \frac{ S^2 } { \frac{ \sqrt{3}} {4} T^2 } = \frac{4}{3} \), or that \( \frac{ S^2 }{ T^2 } = \frac{ \sqrt3 } { 3 } \). Taking square roots on both sides, \( \frac{ S } { T} = \frac1{3^{1/4}} \). \(_\square\)

If a square and a circle have the same perimeter, which of them will have a greater area? ANSWER Let the radius of the circle be \(r\) and the side length of the square be \(s\). Then \[2\pi r=4s \Rightarrow r=\dfrac{2s}{\pi}.\] Now the area of the square is \(s^2,\) and the area of the circle is \(\pi r^2 = \pi \times \left(\dfrac{2s}{\pi}\right)^2=\dfrac{4s^2}{\pi}.\) Then the ratio of the area of the square to the area of the circle is \(\dfrac{s^2}{\hspace{2mm} \frac{4s^2}{\pi}\hspace{2mm} } = \dfrac{\pi}{4} <1.\) Hence, the circle has a larger area. \(_\square\)

Line segments are drawn from the vertices of the large square to the midpoints of the opposite sides to form a smaller, white square.

If each red or blue line-segment measures \(10\) m long, what is the area of the smaller, white square in m\(^{2}?\)

A triangle, a square, a pentagon, a hexagon, an octagon, and a circle all have the same perimeter.

Which one has the smallest area?

Note: All of the polygons are regular.

Four squares of respective side lengths 4, 9,15, and 21 are arranged as shown. Find the length of the yellow line. If your answer can be expressed as \(\frac{a}{7}+\frac{b}{7}\sqrt{c}\), where \(c\) is square free, give \(a+b+c.\)

Note: Neglect the thickness of the lines.

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• Math Article
• Area And Perimeter

Area and Perimeter

Area and perimeter , in Maths, are the two important properties of two-dimensional shapes. Perimeter defines the distance of the boundary of the shape whereas area explains the region occupied by it. 

Area and Perimeter is an important topic in Mathematics, which is used in everyday life. This is applicable to any shape and size whether it is regular or irregular. Every shape has its own area and perimeter formula. You must have learned about different shapes such as triangle, square, rectangle, circle, sphere, etc. The area and perimeter of all shapes are explained here.

What is Area?

The area is the region bounded by the shape of an object. The space covered by the figure or any two-dimensional geometric shape, in a plane, is the area of the shape. The area of all the shapes depends upon their dimensions and properties. Different shapes have different areas.  The area of the square is different from the area of a kite.

If two objects have a similar shape then it’s not necessary that the area covered by them will be equal unless and until the dimensions of both shapes are also equal. Suppose, there are two rectangle boxes, with length as L1 and L2 and breadth as B1 and B2. So the areas of both the rectangular boxes, say A1 and A2 will be equal only if L1=L2 and B1=B2.

What is Perimeter?

Perimeter of a shape is defined as the total distance around the shape. Basically, perimeter is the length of any shape if it is expanded in a linear form. A perimeter is a total distance that encompasses a shape, in a 2d plane. The perimeter of different shapes can match in length with each other depending upon their dimensions.

For example, if a circle is made of a metal wire of length L, then the same wire we can use to construct a square, whose sides are equal in length.

What is the Difference Between Area and Perimeter?

Here is the list of differences between area and perimeter:

Area and Perimeter For all Shapes

There are many types of shapes. The most common ones are Square, Triangle, Rectangle, Circle etc. To know the area and perimeter of all these, we need different formulas.

Perimeter and Area of a Rectangle

A rectangle is a figure/shape with opposite sides equal and all angles equal to 90 degrees. The area of the rectangle is the space covered by it in an XY plane.

where a and b are the length and width of the rectangle.

Perimeter and Area of a Square

A Square is a figure/shape with all four sides equal and all angles equal to 90 degrees. The area of the square is the space occupied by the square in a 2D plane and its perimeter is the distance covered on the outer line.

where a is the length of the side of the square.

Learn more about the perimeter of the square, here.

Perimeter and Area of Triangle

The triangle has three sides. Therefore, the perimeter of any given triangle, whether it is scalene, isosceles or equilateral, will be equal to the sum of the length of all three sides.  And the area of any triangle is the space occupied by it in a plane.

Area and Circumference of Circle

Area of a circle is the region occupied by it in a plane.

In case of a circle, the distance of the outer line of the circle is called the circumference.

Area and Perimeter Formulas

Here is the list of the area and perimeter for different figures in a tabular form. Students can use this table to solve problems based on the formulas given here.

Applications of Area and Perimeter

We know that the area is basically the space covered by these shapes and perimeter is the distance around the shape. If you want to paint the walls of your new home, you need to know the area to calculate the quantity of paint required and cost for the same.

For example, to fence the garden in your house, the length required of the material for fencing is the perimeter of the garden. If it’s a square garden with each side as a cm then the perimeter would be 4a cm. The area is the space contained in the shape or the given figure. It is calculated in square units. Suppose you want to fix tiles in your new home, you need to know the area of the floor to know the no. of tiles required to cover the whole floor. In this article, let us have a look at the formula for area and perimeter of some basic shapes with diagrams and examples.

Area and Perimeter for Grade 4

In Class 4, we will come across the area and perimeter formulas for square and rectangle shapes. Here, the sides of rectangle are measured in inches or feet or yard. Let us see an example.

Example: Find the area of a rectangle with length and width equal to 7ft and 5ft, respectively. Solution: Given, Length = 7ft & Width = 5ft Area of rectangle = Length x Width = 7ft x 5ft = 35 ft 2

Related Articles

Solved examples on area and perimeter.

Here are some solved examples based on the formulas of the area as well as perimeter of different shapes.

If the radius of a circle is 21cm. Find its area and circumference.

Given, radius = 21cm

Therefore, Area =  π × r 2

A = 22/7  × 21 × 21

A = 1386 sq.cm.

Circumference, C =  2πr 

C = 2 x 22/7 x 21 = 132 cm

If the length of the side of a square is 11cm. Then find its area and also find the total length of its boundary.

Given, length of the side, a = 11 cm

Area =  a 2  = 11 2  = 121 sq.cm

Total length of its boundary, Perimeter = 4a = 4 x 11 = 44 sq.cm.

The length of rectangular field is 12m and width is 10m. Find the area of the field along with its perimeter.

Given, Length = 12m

Width = 10m

Therefore, Area = length x width = 12 x 10 = 120 sq.m.

Perimeter = 2 (length + width) = 2 x (12 + 10) = 2 x 22 = 44 m.

Practice Problems (Worksheets)

Solve the questions here based on area and perimeter of different shapes.

• If a square has area 625 sq.m., then find its perimeter.
• The length and width of a rectangle are 11.5 cm and 8.8 cm, respectively. Find its area and perimeter.
• If the height of a triangle is 19cm and its base length is 12cm. Find the area.
• The perimeter of an equilateral triangle is 21cm. Find its area.
• A parallelogram has base length of 16cm and the distance between the base and its opposite side is 7.5cm. Find its area.

Frequently Asked Questions – FAQs

What is the difference between area and perimeter, what is the formula for perimeter, what is the area and perimeter of a circle, what is the perimeter and area example, what is the formula for area of rectangle.

Put your understanding of this concept to test by answering a few MCQs. Click ‘Start Quiz’ to begin!

Select the correct answer and click on the “Finish” button Check your score and answers at the end of the quiz

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Word Problems Worksheets | Area of Rectangles

Promote mathematical interest in children of grade 3 through grade 6 by relating the concept to the real-life situation with this batch of printable word problems worksheets on area of rectangles. The word problems offer two levels of difficulty; level 1 comprises word problems to find the area of rectangles and the missing parameters, while level 2 has scenarios to find the area involving unit conversions or finding the cost. Also, included here are word problems to find the area of rectangular shapes. Delve into practice with the free worksheets here!

Area Word Problems | Level 1

Equip children to bring together reality and math with these pdf word problems on area of rectangles. Instruct 3rd grade and 4th grade kids to plug in the dimensions in the formula A = length * width to compute the area.

• Download the set

Area Word Problems | Level 2

Visualize the scenario and highlight the length and width. Children are expected to convert to the specified units and then solve for the area of rectangles. Some word problems require calculating the cost.

Find the Missing Length or Width | Level 1

Direct children of grade 4 and grade 5 to figure out the area and the length or width in each word problem. Rearrange the rectangle formula, making the missing dimension the subject, substitute and solve for length or width.

Find the Missing Length or Width | Level 2

Level up with this set of printable worksheets featuring word problems to solve for the unknown dimension using the area and the dimension given. The word problems involve either unit conversion or determining the cost to provide ample practice for 5th grade and 6th grade children.

Area of Rectangular Paths | Word Problems

Read the scenario and draw the rectangular path, decompose the path into non-overlapping rectangles and find the area of each individual rectangle, add the areas to determine the area of the rectangular paths in this set of pdf worksheets.

Related Worksheets

» Area of Squares

» Area of Parallelograms

» Area of Quadrilaterals

» Area of Polygons

» Rectangles

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AREA AND PERIMETER WORD PROBLEMS

Problem 1 :

The length of a rectangle is 4 less than 3 times its width. If its perimeter is 32 cm, then find the area of the rectangle.

Let x be the width of the rectangle.

Then, its length is (3x - 4).

Perimeter of the rectangle is 32 cm

2(l + w) = 32

3x - 4 + x = 16

4x - 4 = 16

And length of the rectangle is

Formula for area of a rectangle :

=  l ⋅ w

Area = 55 cm 2

Problem 2 :

Theresa wants new carpeting for her family room. Her family room is a 12 ft by 21 ft rectangle. How much carpeting does she need to buy to cover her entire family room ?

To find the amount of carpet required, we have to know its area. Because the family room is in rectangle shape, we can use the formula for area of a rectangle to find the area of the family room.

Substitute 12 for l and 21 for w.

So, T heresa needs to buy 252 square ft carpeting  to cover her entire family room.

Problem 3 :

Lily to wants to do fencing around a circular garden that has a radius of 70 m. If the cost of fencing is $12 per meter, find the total cost of fencing for the entire garden (Use  π  =  22/7) .

Fencing is done around the circular garden. To find the total cost of fencing, we have to know the perimeter of the garden, Because the garden is in the shape of circle, we can use the formula for perimeter of a circle to find the perimeter of the garden.

Formula for perimeter of a circle :

Substitute 22/7 for  π and 70 for r.

= 2( 22/7)( 70)

So, the perimeter of the garden is 440 meters.

The cost of fencing is $12 per meter.

Then, the total cost of fencing for 440 meters :

Problem 4 :

If the cost of the carpeting is $15 per square meter, find the total cost of carpeting the floor of the room whose shape is a regular pentagon shown below.

To find the total cost of carpeting the floor of the room, we have to know its area. Because the floor of the room is in the shape of regular pentagon (regular polygon), we can use the formula for area of a regular polygon to find the area of the floor.

Formula for area of a regular polygon :

= 1/2(apothem)(perimeter of polygon) ----(1)

In the above regular pentagon, apothem is 4 m

The perimeter of a regular polygon is

= (No. of sides)(Length of each side)

Therefore, the perimeter of the regular pentagon shown above is 

To find the area of the regular pentagon, substitute 4 for apothem and 30 for perimeter in the formula (1).

(1) ----> = 1/2(4)(30)

The cost of carpeting is $15 per square meter.

Then, the total cost of carpeting for 60 square meters :

Problem 5 :

The poster has a border whose width is 2 cm on each side. If the printed material has the length of 6 cm and width of 8 cm, then find the area of the border.

Draw a sketch

In the above diagram, to find the area of the border, we have to subtract the area of the printed material from the complete area of the poster.

Complete area of the poster :

= l  ⋅  w

Substitute 10 for l and 12 for w.

= 10  ⋅ 12

Area of the printed material :

Substitute 6 for l and 8 for w.

Area of the border :

= Area of the poster - Area of the printed material

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Teach Think Elementary

Content, not just cute., area and perimeter relationships & problem solving, part 5.

Area and Perimeter are difficult math concepts that kids usualy learn in upper elementary. As teachers, it can feel overwhelming to tackle all of that content. I’m breaking down the perimeter and area standards into manageable chunks in this blog post series.

Part 1:Teaching Area Concepts

Part 2: Measuring Area & Multiplication

3: Composing & Decomposing Area and The Distributive Property (coming soon!)

Part 4: Teaching Perimeter

This is Part 5: Area & Perimeter Relationships and Problem Solving

Geometric measurement: recognize perimeter as an attribute of plane figures and distinguish between linear and area measures.

8. Solve real world and mathematical problems involving perimeters of polygons, including finding the perimeter given the side lengths, finding an unknown side length, and exhibiting rectangles with the same perimeter and different areas or with the same area and different perimeters

I’ve broken perimeter down into two sections here. Part 4 was understanding perimeter and solving problems with perimeter on its own. In this part, we’ll tackle the relationship with area and perimeter. But it’s much easier to understand the relationship between area and perimeter if you’re familiar with both of those things first, of course!

This is another fun one, in my opinion! It’s time to make lots of rectangles and explore and figure things out, and that’s my favorite kind of math. 

Overwhelmed?? I’ve spent hours and hours (like soooo many hours) thinking about this and creating a math unit so you don’t have to. Get my Perimeter & Area Math Unit here .

Concept: distinguish between linear and area measures. 

If you’ve been playing along at home, this one should be pretty much done at this point! I always introduced this in the beginning, before even teaching area . That seems important to me because up until this point, kids have only really worked with linear measurement. I like to make it clear to them at the beginning of the unit that we’re now in uncharted waters and learning a new way of measuring. (They’ll learn a third way in 5th grade, when they tackle volume.) 

Concept: rectangles with the same perimeter and different areas and vice versa. 

The goal here is for kids to look for the relationship and to make generalizations about the relationship between area and perimeter. 

This is a fun concept that gives kids a chance to explore and come up with their own ideas and understandings. 

If you need an idea for how to manage all of this exploration, here’s what I did:

-break the kids up into groups of 2-4. 

-assign each group an area or perimeter to investigate. (Definitely do these on two different days!!)

-give them scissors, crayons, and lots and lots of grid paper.

-let them see how many different rectangles they can make with their assigned perimeter or area. 

-give them a chance to present their findings to the group. If you have a class that large or you’re short on time, they can make a display on a desk or bulletin board and the other students can circulate, museum-style. 

-lead a conversation about how they figured out the rectangles, how do they know they have them all, what did they find, etc. 

-Kids can write exit tickets with their ideas for accountability & assessment. 

-After you’ve had one day with same perimeters and one day with same areas, have the kids compare the two and discuss if they see any relationships. 

**the question will inevitably come up of whether 5×8 and 8×5 are the same rectangle or not, and that will lead to plenty of good discussions. The answer doesn’t really matter, in my opinion, but it’s a great way for kids to think critically and develop deeper concepts. 

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Area and perimeter problem solving

Subject: Mathematics

Age range: 5-7

Resource type: Lesson (complete)

Last updated

25 January 2018

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Really great challenging problems that have helped me get better on the are and perimeter topic

A real-time saver and some very challenging problems thank you

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