# Unit 9 Section 3 : Area and Perimeter of a Rectangle

In a rectangle we can still find the area by counting squares, but we can also multiply the two lengths together.
For example: We can see that the area is 10 cm² by counting squares, but if we multiply the lengths:

5 cm × 2 cm = 10 cm²

We have to be careful to use the same units when doing calculations.

• If the lengths are in cm then the answer will be in cm².
• If the lengths are in mm then the answer will be in mm².
• If the lengths are in m then the answer will be in .
If the lengths are not in the same units we must convert them using the rules in the previous section.

## Different Area Units

Although 1 centimetre is equal to 10 millimetres, 1 cm² is not equal to 10 mm².

A square which is 1cm × 1cm has area 1cm².
The same square is 10mm × 10mm, and 10×10=100, so its area is 100 mm². Similarly, a square which is 1m × 1m has area 1m².
The same square is 100cm × 100cm, and 100×100=10000, so its area is 10000 cm². Be careful to remember these facts whenever you are converting the units of an area.

## Example Question

Look at the rectangle on the grid below. Each square on the grid is 1cm × 1cm. Practice Questions Do each of these questions then click on the button marked to see whether you are correct. The rectangle measures 3cm × 4cm so the area is 12 cm². (a) Convert this into an area in mm². (b) Find the area in mm² by converting the lengths to mm first. ## Exercises

Work out the answers to the questions below and fill in the boxes. Click on the button to find out whether you have answered correctly. If you are right then will appear and you should move on to the next question. If appears then your answer is wrong. Click on to clear your original answer and have another go. If you can't work out the right answer then click on to see the answer.

Question 1
Find the areas (in cm²) and perimeters (in cm) of the rectangles below.
The squares on each grid are 1cm × 1cm.

 (a) Area = cm²  Perimeter = cm  (b) Area = cm²  Perimeter = cm  (c) Area = cm²  Perimeter = cm  (d) Area = cm²  Perimeter = cm  Question 2
Find the areas and perimeters of the rectangles below.
The diagrams have not been drawn accurately.

 (a) Area = cm²  Perimeter = cm  (b) Area = cm²  Perimeter = cm  (c) Area = mm²  Perimeter = mm  (d) Area = cm²  Perimeter = cm  (e) Area = mm²  Perimeter = mm  (f) Area = m²  Perimeter = m  Question 3
Look at the rectangle below. (a) Find the area of the rectangle in cm². cm²  (b) Find the area of the rectangle in m². m²  (c) Find the perimeter of the rectangle in cm. cm  (d) Find the perimeter of the rectangle in m. m  Question 4
Find the area of this rectangle in mm² and cm². mm²  cm²  Question 5
A rectangle has an area of 48 cm². The length of one side is 6 cm.

What is the perimeter of the rectangle?
cm  Question 6
A rectangle has a perimeter of 24 cm and an area of 32 cm².

What are the lengths of the sides of the rectangle?

The longer side is cm
The shorter side is cm  You have now completed Unit 9 Section 3
 Your overall score for this section is Correct Answers You answered questions correctly out of the questions in this section. Incorrect Answers There were questions where you used the Tell Me button. There were questions with wrong answers. There were questions you didn't attempt.
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Produced by A.J. Reynolds January 2001