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Area and Perimeter of a Rectangle

Questions on the areas and perimeters of rectangles which will test your problem solving abilities.

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This is level 2: find the dimensions of rectangles given their areas and perimeters. You can earn a trophy if you get at least 7 questions correct and you do this activity online. The diagrams are not drawn to scale.

1. Find the shortest side of a rectangle if its area is 16 square centimetres and its perimeter is 20 centimetres.

Area = 16cm2
Perimeter = 20cm

Working:

cm Correct Wrong

2. Find the shortest side of a rectangle if its area is 36 square centimetres and its perimeter is 26 centimetres.

Area = 36cm2
Perimeter = 26cm

Working:

cm Correct Wrong

3. Find the longest side of a rectangle if its area is 112 square metres and its perimeter is 44 metres.

Area = 112m2
Perimeter = 44m

Working:

m Correct Wrong

4. Find the longest side of a rectangle if its area is 24 square metres and its perimeter is 28 metres.

Area = 24m2
Perimeter = 28m

Working:

m Correct Wrong

5. Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 1677 square milimetres and its perimeter is 164 milimetres.

Area = 1677mm2
Perimeter = 164mm

Working:

mm Correct Wrong

6. Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 1036 square milimetres and its perimeter is 130 milimetres.

Area = 1036mm2
Perimeter = 130mm

Working:

mm Correct Wrong

7. A rectangle's length is 5cm longer than its width. Its area is 644cm². What is it's width?

Working:

cm Correct Wrong

8. A rectangle's width is 6m shorter than its length. Its perimeter is 160m. What is it's length?

Working:

m Correct Wrong

9. The numerical value of the area of a square is 8 times bigger than its perimeter when measured using the centimetres. How long is the side of this square?



SQUARE

Area = 8 × Perimeter

Working:

cm Correct Wrong

10. This last question is about a cuboid. Find the shortest side of a cuboid if its volume is 40 cubic feet and its surface area is 76 square feet. You might also find it helpful to know that the sum of the length of all 12 sides is 44 feet.Cube

Working:

feet Correct Wrong
Check

This is Area and Perimeter of a Rectangle level 2. You can also try:
Area Builder Level 1 Investigation

Instructions

Try your best to answer the questions above. Type your answers into the boxes provided leaving no spaces. As you work through the exercise regularly click the "check" button. If you have any wrong answers, do your best to do corrections but if there is anything you don't understand, please ask your teacher for help.

When you have got all of the questions correct you may want to print out this page and paste it into your exercise book. If you keep your work in an ePortfolio you could take a screen shot of your answers and paste that into your Maths file.

Why am I learning this?

Mathematicians are not the people who find Maths easy; they are the people who enjoy how mystifying, puzzling and hard it is. Are you a mathematician?

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Description of Levels

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Area Builder - An interactive workspace in which to make shapes using square tiles with given areas and perimeters.

Level 1 - Find the perimeters and areas of rectangles

Level 2 - Find the dimensions of rectangles given their areas and perimeters

Area Maze - These are brilliant! When you think you know the formula for the area of a rectangle these puzzles will give you quite a challenge.

Investigation - The perimeter of a rectangle is 28cm. What could its area be?

More on this topic including lesson Starters, visual aids and investigations.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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Curriculum Reference

See the National Curriculum page for links to related online activities and resources.

Area and Perimeter poster

Help Video

Don't wait until you have finished the exercise before you click on the 'Check' button. Click it often as you work through the questions to see if you are answering them correctly. You can double-click the 'Check' button to make it float at the bottom of your screen.

Answers to this exercise are available lower down this page when you are logged in to your Transum account. If you don’t yet have a Transum subscription one can be very quickly set up if you are a teacher, tutor or parent.

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