Areas and Volumes.

1. Area

Area is the amount of space that is enclosed within a 2-D shape. There are many units of area, some common metric ones are : mm2, cm2, km2

You may have used other imperial units such as square inches, square feet, square yards and square miles. We’ll concentrate on the metric units in this worksheet.

Area of a rectangle :

This is calculated by multiplying the width of the shape by the length.

Example : Calculate the area of the shape shown :

13cm

5cm

not to scale

Area = 13 x 5 = 65cm2


Area of a triangle

This is calculated by multiplying half of the length of the base by the height.

Example : Calculate the area of the shape shown :

Area = ½ x 6 x 7

= 3 x 7

7cm = 21cm2

6cm not to scale

When calculating the area of a triangle, make sure you use the height and not the length of one of the sides :

height

5cm 4cm

not to scale

Some difficult shapes

Some questions will not just involve one shape but maybe 2 or 3, like this :

Example : Calculate the area of the shape shown :

6cm

3cm

7cm

not to scale

14cm

We first have to split the large “L” shaped figure into two separate rectangles and work out the sides that we need to calculate the area like this :

6cm

3cm

7cm

14 - 6 = 8cm 7 - 3 = 4cm

not to scale

14cm

Now we have two rectangles we can work out the area of each rectangle and add the two areas together to get the area of the L-shape like this :

Area = 6 x 7 = 42cm2

Area = 8 x 4 = 32cm2

Total area = 42 + 32 = 74cm2

Volume

This is the amount of space enclosed within a 3-D object. Common units are cm3, m3 and km3. Note also that cm3 can also be described as litres.

Example Find the volume of this cuboid :

5cm

12cm

10cm

not to scale

To find the volume of a cuboid we use :

Volume of a cuboid = height x width x length

In this case : Volume = 5 x 10 x 12 = 600cm3

Exercise 7.1

1. Work out the area of this shape :

4cm

12cm not to scale


2. The plan view of a hotel room is shown below. Find the area of the floor.

4m

not to scale

4m

3m

7m

3. A triangular road sign has a base dimension of 60cm and a height of 60cm.

Work out its area in

(a) cm2 (b) m2 (hint convert 60cm to m first)

4. A small aircraft has passenger windows that are squares with sides of 40cm.

(a) Work out the area of each window in cm2

(b) If there are 50 windows, find the total area of glass in square metres.

(c) The front windscreen of the aircraft is a rectangle as shown below :

Calculate the area of

1.2m the windscreen in m2

not to scale

2m

5. Fabien wants to fill this cake tin with mixture. How does he calculate the correct volume of the cake mixture?

6cm

20cm

not to scale

20cm

(a) 20 + 20 + 6 (b) 20 + 20 + 6 x 2

(c) 20 x 2 x 6 (d) 20 x 20 x 6

6. The units for measuring the volume of the cake mixture in Q5 are :

(a) cm3 (b) cm2 (c) cm (d) m3

7. A swimming pool has a constant depth of 2m. It is 25m long and 10m wide. Calculate the volume of water required to completely fill it.

8. The waiting room at an airport is a cube with the dimensions of 9m.

(a) What is the area of one of the walls?

(b) What is the area of all 4 walls?

(c) What is the total area of the four walls and the ceiling together?

(d) If one tin of paint will cover 50m2, then how many tins are needed to paint the 4 walls and ceiling?

(e) What is the volume of the room?

9. A notice board has to have an area of 9 square metres. The board measures 1.5m from top to bottom as shown. What is the length of the board?

Length = ???

1.5m Area = 9m2


10. This is a drawing of a lawn and patio in a garden :

7m

PATIO

8m

LAWN 6m

not to scale

10m

(i) Which of these is the correct way to find the area of the lawn?

(a) (6 x 8) + (7 x 10) (b) (7 x 8) + (3 x 2)

(c) (8 x 7) + (6 x 3) (d) (10 x 6) + (8 x 7)

(ii) Calculate the area of the patio.

Worksheet taken from :

www.gcad-cymru.org.uk/vtc/ngfl/<wbr>key_skills/20040825/018_area_and_<b>volume</b>.doc -