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 48 square centimetres and its perimeter is 28 centimetres.

Area = 48cm2
Perimeter = 28cm

Working:

cm Correct Wrong

2. Find the shortest side of a rectangle if its area is 24 square centimetres and its perimeter is 20 centimetres.

Area = 24cm2
Perimeter = 20cm

Working:

cm Correct Wrong

3. Find the longest side of a rectangle if its area is 84 square metres and its perimeter is 40 metres.

Area = 84m2
Perimeter = 40m

Working:

m Correct Wrong

4. Find the longest side of a rectangle if its area is 14 square metres and its perimeter is 18 metres.

Area = 14m2
Perimeter = 18m

Working:

m Correct Wrong

5. Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 1209 square milimetres and its perimeter is 140 milimetres.

Area = 1209mm2
Perimeter = 140mm

Working:

mm Correct Wrong

6. Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 1064 square milimetres and its perimeter is 132 milimetres.

Area = 1064mm2
Perimeter = 132mm

Working:

mm Correct Wrong

7. A rectangle's length is 3cm longer than its width. Its area is 1258cm². What is it's width?

Working:

cm Correct Wrong

8. A rectangle's width is 3m shorter than its length. Its perimeter is 142m. What is it's length?

Working:

m Correct Wrong

9. The numerical value of the area of a square is 6 times bigger than its perimeter when measured using the centimetres. How long is the side of this square?



SQUARE

Area = 6 × Perimeter

Working:

cm Correct Wrong

10. This last question is about a cuboid. Find the shortest side of a cuboid if its volume is 168 cubic feet and its surface area is 188 square feet. You might also find it helpful to know that the sum of the length of all 12 sides is 68 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.

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This web site contains over a thousand free mathematical activities for teachers and pupils. Click here to go to the main page which links to all of the resources available.

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Comment recorded on the 3 October 'Starter of the Day' page by S Mirza, Park High School, Colne:

"Very good starters, help pupils settle very well in maths classroom."

Comment recorded on the 11 January 'Starter of the Day' page by S Johnson, The King John School:

"We recently had an afternoon on accelerated learning.This linked really well and prompted a discussion about learning styles and short term memory."

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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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