Unit 9 Section 2 : Area and Perimeter of a Square

In this section we bring in standard units for measuring area and perimeter.
From now on you should always put units in your answers.

The area of a square with sides of length 1cm is 1cm².

The area of other squares can be found by counting squares or by multiplying the length of the sides.


The perimeter of a square is the total length of the four sides.

Example Question

Look at the 7cm × 7cm square below:
Practice Questions
Work out the answer to 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.

(a) What is the area of the square?

(b) What is the perimeter of the square?

NOTE: The area is given in cm² but the perimeter is given in cm because it is a length.

Different Length Units

We also measure in metres (m) and millimetres (mm). These are converted as follows:

To convert from cm to mm we multiply by 10. To convert from mm to cm we divide by 10.
To convert from cm to m we divide by 100. To convert from m to cm we multiply by 100.
For example:

 

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
Work out the area and perimeter of each of the squares below.
Each square on the grid is 1cm by 1cm.

(a)
Area = cm²
Perimeter = cm
(b)
Area = cm²
Perimeter = cm
(c)
Area = cm²
Perimeter = cm

Question 2
Answer the questions below.

(a) The sides of a square are 10 cm long. What is its area?
cm²
(b) The sides of a square are 8 cm long. What is its area?
cm²
(c) The sides of a square are 9 cm long. What is its area?
cm²
(d) The sides of a square are 12 cm long. What is its area?
cm²

Question 3
Answer the questions below.

(a) The sides of a square are 15 cm long. What is its perimeter?
cm
(b) The sides of a square are 20 cm long. What is its perimeter?
cm
(c) The sides of a square are 13 cm long. What is its perimeter?
cm
(d) The sides of a square are 16 cm long. What is its perimeter?
cm

Question 4
Below are some conversions between metres, centimetres and millimetres. Fill in the gaps.

(a) 3.2 cm = mm
(b) 28 mm = cm
(c) 152 cm = m
(d) 1.71 m = cm
(e) 216 mm = cm
(f) 0.07 m = cm

Question 5
A square has sides of length 20mm.

(a) Find the area of the square in mm².
mm²

(b) Find the area of the square in cm². You may find it helpful to draw the square on a piece of paper.
cm²

Question 6
The perimeter of a square is 40 cm.

How long are its sides?
cm

Question 7
The area of a square is 36 cm².

How long are its sides?
cm

Question 8
The perimeter of a square is 44 cm.

What is its area?
cm²

Question 9
The area of a square is 144 cm².

What is its perimeter?
cm


You have now completed Unit 9 Section 2
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Produced by A.J.Reynolds January 2001