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 -