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 cm by counting squares, but if we multiply the lengths:

5 cm 2 cm = 10 cm

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

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 cm is not equal to 10 mm.

A square which is 1cm 1cm has area 1cm.
The same square is 10mm 10mm, and 1010=100, so its area is 100 mm.

Similarly, a square which is 1m 1m has area 1m.
The same square is 100cm 100cm, and 100100=10000, so its area is 10000 cm.

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 Click on this button below to see the correct answer to see whether you are correct.

The rectangle measures 3cm 4cm so the area is 12 cm.

(a) Convert this into an area in mm.

(b) Find the area in mm by converting the lengths to mm first.

 

Exercises

Work out the answers to the questions below and fill in the boxes. Click on the Click this button to see if you are correct 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 Click on this button to see the correct answer to see the answer.

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

(a)
Area = cm
Perimeter = cm
(b)
Area = cm
Perimeter = cm
(c)
Area = cm
Perimeter = cm
(d)
Area = cm
Perimeter = cm

Question 2
Find the areas and perimeters of the rectangles below.
The diagrams have not been drawn accurately.

(a)
Area = cm
Perimeter = cm
(b)
Area = cm
Perimeter = cm
(c)
Area = mm
Perimeter = mm
(d)
Area = cm
Perimeter = cm
(e)
Area = mm
Perimeter = mm
(f)
Area = m
Perimeter = m

Question 3
Look at the rectangle below.
(a) Find the area of the rectangle in cm.
cm

(b) Find the area of the rectangle in m.
m

(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 mm and cm.
mm

cm

Question 5
A rectangle has an area of 48 cm. 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 cm.

What are the lengths of the sides of the rectangle?

The longer side is cm
The shorter side is cm


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Produced by A.J.Reynolds January 2001