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 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 24 square centimetres and its perimeter is 22 centimetres.

Area = 24cm2
Perimeter = 22cm

Working:

cm Correct Wrong

2. Find the shortest side of a rectangle if its area is 54 square centimetres and its perimeter is 30 centimetres.

Area = 54cm2
Perimeter = 30cm

Working:

cm Correct Wrong

3. Find the longest side of a rectangle if its area is 190 square metres and its perimeter is 58 metres.

Area = 190m2
Perimeter = 58m

Working:

m Correct Wrong

4. Find the longest side of a rectangle if its area is 70 square metres and its perimeter is 34 metres.

Area = 70m2
Perimeter = 34m

Working:

m Correct Wrong

5. Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 1862 square milimetres and its perimeter is 174 milimetres.

Area = 1862mm2
Perimeter = 174mm

Working:

mm Correct Wrong

6. Find the difference between the lengths of the longest and shortest sides of a rectangle if its area is 1320 square milimetres and its perimeter is 146 milimetres.

Area = 1320mm2
Perimeter = 146mm

Working:

mm Correct Wrong

7. A rectangle's length is 4cm longer than its width. Its area is 837cm². What is it's width?

Working:

cm Correct Wrong

8. A rectangle's width is 4m shorter than its length. Its perimeter is 144m. What is it's length?

Working:

m Correct Wrong

9. The numerical value of the area of a square is 4 times bigger than its perimeter when measured using the centimetres. How long is the side of this square?



SQUARE

Area = 4 × Perimeter

Working:

cm Correct Wrong

10. This last question is about a cuboid. Find the shortest side of a cuboid if its volume is 108 cubic feet and its surface area is 144 square feet. You might also find it helpful to know that the sum of the length of all 12 sides is 60 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

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.

Please contact me if you have any suggestions or questions.

Email address

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 16 March 'Starter of the Day' page by Mrs A Milton, Ysgol Ardudwy:

"I have used your starters for 3 years now and would not have a lesson without one! Fantastic way to engage the pupils at the start of a lesson."

Comment recorded on the 17 June 'Starter of the Day' page by Mr Hall, Light Hall School, Solihull:

"Dear Transum,

I love you website I use it every maths lesson I have with every year group! I don't know were I would turn to with out you!"

Each month a newsletter is published containing details of the new additions to the Transum website and a new puzzle of the month.

The newsletter is then duplicated as a podcast which is available on the major delivery networks. You can listen to the podcast while you are commuting, exercising or relaxing.

Transum breaking news is available on Twitter @Transum and if that's not enough there is also a Transum Facebook page.

Featured Activity

Triangle Solver

Triangle Solver

This simple calculator will work out the lengths of the sides and the size of the angles of any triangle given thee particular pieces of information.

Answers

There are answers to this exercise but they are available in this space to teachers, tutors and parents who have logged in to their Transum subscription on this computer.

A Transum subscription unlocks the answers to the online exercises, quizzes and puzzles. It also provides the teacher with access to quality external links on each of the Transum Topic pages and the facility to add to the collection themselves.

Subscribers can manage class lists, lesson plans and assessment data in the Class Admin application and have access to reports of the Transum Trophies earned by class members.

If you would like to enjoy ad-free access to the thousands of Transum resources, receive our monthly newsletter, unlock the printable worksheets and see our Maths Lesson Finishers then sign up for a subscription now:

Subscribe

Go Maths

Learning and understanding Mathematics, at every level, requires learner engagement. Mathematics is not a spectator sport. Sometimes traditional teaching fails to actively involve students. One way to address the problem is through the use of interactive activities and this web site provides many of those. The Go Maths page is an alphabetical list of free activities designed for students in Secondary/High school.

Maths Map

Are you looking for something specific? An exercise to supplement the topic you are studying at school at the moment perhaps. Navigate using our Maths Map to find exercises, puzzles and Maths lesson starters grouped by topic.

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:

Alternatively, if you use Google Classroom, all you have to do is click on the green icon below in order to add this activity to one of your classes.

It may be worth remembering that if Transum.org should go offline for whatever reason, there are mirror sites at Transum.com and Transum.info that contain most of the resources that are available here on Transum.org.

When planning to use technology in your lesson always have a plan B!

Do you have any comments? It is always useful to receive feedback and helps make this free resource even more useful for those learning Mathematics anywhere in the world. Click here to enter your comments.

Apple

©1997-2021 WWW.TRANSUM.ORG

© 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

Close

Close

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 Mazes - 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.

Log in Sign up

Curriculum Reference

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

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.

Log in Sign up

Close

Close