Area

The amount of surface covered by each shape is called its area.

Which one of these carpets takes up more floor space?They have the same area.

The usual way of measuring area is to find the number of squares a shape covers

1 cm

1cm

Here we have a square measuring 1 cm by 1 cm

We say the square has an area of 1 2cm

1 cm

1cm

2 cm

2 cm

Here we have a square measuring 2 cm by 2 cmIf we place it on some centimetre squared paper we can see it covers 4 squares

We say the square has an area of 4 2cm

What is the area of the following rectangles?

A B C

AB

C

Placing each one onto centimetre paper we have:

The area of rectangle A is 6 2cmThe area of rectangle B is 24 2cmThe area of rectangle C is 12 2cm

AB

C3 cm

2 cm

6 cm

4 cm

2 cm

6 cm

The area of a rectangle

Length = 3 cm Width = 2 cm

The area of rectangle A is 23 2 6cm

Length = 6 cm Width = 4 cm

The area of rectangle B is 26 4 24cm

Length = 2 cm Width = 6 cm

The area of rectangle C is 22 6 12cm

Length (l)

Width (w)Area length width

lw

The area of a rectangle

Area of a triangleDraw a triangle onto squared paperDraw a rectangle around it

Notice the area of the rectangle is base height2Area 14 8 112cmbh

base

height

Cut out the shaded area and place onto the left part of the triangle.Cut out the shaded area and place onto the right part of the triangle.

What do you notice?

height

We notice the area of the triangle is 1

base height2

21 1

Area 14 82 2

56cmbh

base

height

Area of a triangle

base

height

Area of a triangle

1

2A bh

Area of a parallelogram

base

height

base

height

A parallelogram is a quadrilateral, which its opposite sides are parallel but are of unequal length

Consider the shaded part and cut it off and place it on the other side.

What do you notice?

The area of the parallelogram is base height.

base (b)

height (h)

Area of a parallelogram

The area of a parallelogram is base height

bh

h

a

b

Split the trapezium into two triangles

Area of a trapezium

Area of triangle A1

2ah Area of triangle B

1

2bh

Split the trapezium into two triangles

h

b

h

a

AB

Area of trapezium 1 1 1

2 2 2ah bh a b h

Area of a trapezium

To find the area of a trapezium you must add together the two parallel sides, multiply by the height and divide by 2.

1

2A a b h

h

a

b

The area of a kite

Draw a kite onto squared paperDraw on diagonal length aDraw on diagonal length b.Cut out shaded triangle.Place the triangle on the other side.Cut out the shaded triangle.Place this triangle on the other side.

a

b

Your diagram should look like this.

a

b

The area of a kite

1

2a

b

The length (l) is 1

2a

The width (w) is b

The area

1

2

lw

ab

What do you notice? We now have a rectangle

b

a

The area of a kite

Area of a kite is half the product of its diagonals

1

2A ab

length (l)

width (w)

A lw1

2A bh

base (b)

height (h)

base (b)

height (h)

A bh

h

a

b

1

2A a b h

b

a 1

2A ab

Area of Shapes

Rectangle Triangle Parallelogram

Trapezium Kite