Transum Software

Area and Perimeter of a Rectangle

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

Area Builder Level 1 Level 2 Investigation Description Help Video More Measures

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 66 square centimetres and its perimeter is 34 centimetres.

Area = 66cm2
Perimeter = 34cm

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 105 square metres and its perimeter is 44 metres.

Area = 105m2
Perimeter = 44m

Working:

m Correct Wrong

4. Find the longest side of a rectangle if its area is 152 square metres and its perimeter is 54 metres.

Area = 152m2
Perimeter = 54m

Working:

m Correct Wrong

5. Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 1353 square milimetres and its perimeter is 148 milimetres.

Area = 1353mm2
Perimeter = 148mm

Working:

mm Correct Wrong

6. Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 825 square milimetres and its perimeter is 116 milimetres.

Area = 825mm2
Perimeter = 116mm

Working:

mm Correct Wrong

7. A rectangle's length is 6cm longer than its width. Its area is 667cm². What is it's width?

Working:

cm Correct Wrong

8. A rectangle's width is 6m shorter than its length. Its perimeter is 168m. What is it's length?

Working:

m Correct Wrong

9. The numerical value of the area of a square is 3 times bigger than its perimeter when measured using the centimetres. How long is the side of this square?



SQUARE

Area = 3 × 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.

Transum.org

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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?

Comment recorded on the 12 July 'Starter of the Day' page by Miss J Key, Farlingaye High School, Suffolk:

"Thanks very much for this one. We developed it into a whole lesson and I borrowed some hats from the drama department to add to the fun!"

Comment recorded on the 14 September 'Starter of the Day' page by Trish Bailey, Kingstone School:

"This is a great memory aid which could be used for formulae or key facts etc - in any subject area. The PICTURE is such an aid to remembering where each number or group of numbers is - my pupils love it!
Thanks"

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Teachers

If you found this activity useful don't forget to record it in your scheme of work or learning management system. The short URL, ready to be copied and pasted, is as follows:

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© Transum Mathematics :: This activity can be found online at:
www.transum.org/Software/SW/Starter_of_the_day/students/Oblongs.asp?Level=2

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

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.

Help Video

This video is from the Mometrix Academy.

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.

Log in Sign up

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