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KS3 Bitesize

Maths

Area

The area of a shape is a measure of the 2 dimensional space that it covers. Area is measured in squares - eg square cm, square metres and square km.

Introduction

This Revision Bite covers:

Counting squares

A 1cm x 1cm shaded area

A square cm has a length of 1 cm. We say that it has an area of 1 cm2 ( 1 cm squared).

A 3cm x 2cm shaded area

This rectangle contains six squares. Each of the squares has an area of 1cm2, so the area of the rectangle is 6cm2.

Question

By counting the squares, find the area of the following shapes:

a)
b)

A shaded area
A shaded area
Answer

a) 10cm2
b) 8cm2
Remember, there are six whole squares and four half squares in the triangle.

Rectangles

area = length (l) x bredth (b)

Another way to find the area of a rectangle is to multiply its length by its width.

The formula is: area = length × width

We can rearrange this formula to find the length or the width:

length = area ÷ width

width = area ÷ length

Question

What is the length of this rectangle?

Area = 56cm squared and height = 7cm
Answer

The area is 56cm2 and the width is 7cm, so the length is 56 ÷ 7 = 8cm

Triangles

Look at the triangle below:

Area of a triangle

If you multiply the base by the perpendicular height, you get the area of a rectangle. The area of the triangle is half the area of the rectangle.

So to find the area of a triangle, multiply the base by the perpendicular height and divide by two. The formula is:

Area = (b × h)/2

Question

Find the area of this triangle:

Base 8cm and Height 5cm
Answer

The area of the triangle is:
(5 × 8)/2 = 40/2 = 20cm2

Compound shapes

There are two different methods for finding the area of this shape:

Area of a compound

Method 1

Divide the shape into squares and rectangles, find their individual areas and then add them together.

Area = 16 + 16 + 48 = 80cm squared

Area = 16 + 16 + 48 = 80cm2

Method 2

Imagine the shape as a large rectangle with a section cut out.

Find the area of the large rectangle (12 × 8) and then subtract the part that has been cut out (4 × 4)

Area = 16 + 16 + 48 = 80 cm squared

Area = (12 × 8) - (4 × 4) = 96 - 16 = 80cm2

Parallelograms

The area of a parallelogram is the base × perpendicular height (b × h).

area = base (b) x height (h)

You can see that this is true by rearranging the parallelogram to make a rectangle.

Rearranging a parallelogram

Area of a parallelogram

Regular parallelogram showing base and height.

Rearranging a parallelogram

Area of a parallelogram

Section to move is highlighted

Rearranging a parallelogram

Area of a parallelogram

Highlighted section is moved to form rectangle.

Use the perpendicular height of the parallelogram, not the sloping height.

Question

Find the area of this parallelogram:

Answer

The answer is 21cm2.
Remember to use the perpendicular height.

Parallelograms

You now know how to find the area of a parallelogram, but what happens if you need to find the base or the height? You just have to rearrange the formula.

A = b × h

h = A ÷ b

b = A ÷ h

Question
Area of a parallelogram

Q1. The area of this parallelogram is 12cm2. What is its perpendicular height?

Q2. Find the length of the base of this parallelogram:

Area of a parallelogram. Area = 40 cm squared
Answer

A1. h = A ÷ b
h = 12 ÷ 4 = 3cm

A2. b = A ÷ h
b = 40 ÷ 5 = 8cm

Remember to divide the area by the perpendicular height.

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