Area and perimeter The perimeter of a shape is easy to work out. It is just the distance all the way round the edge. If the shape has straight sides, add up the lengths of all the sides. These may be given, or you may need to measure carefully along each of the sides using a ruler. 3 cm 5 cm 4 cm 6 cm 3 cm + 5 cm + 4 cm + 6 cm = 18 cm April 2008. Kindly contributed to the Adult Basic Skills Resource Centre http://www.skillsworkshop.org by Julie Hobson, Northern Learning Trust. Main curriculum links MSS1/L1.8 Work out the perimeter of simple shapes. (a) know that perimeter is the boundary of a shape (b) know that perimeter is measured in units of length (c) understand that measurements required to calculate the length of the perimeter depend on the shape MSS1/L1.9 Work out the area of a rectangle. (a) know that area is a measure of surface (b) know what measurements are required to calculate area, and how to obtain them (c) know that measurements must be in the same units before calculating area (d) know that the area of a rectangle = length x width (e) know that area is measured in square units MSS1/L1.10  Work out simple volume (e.g. cuboids) (a) know that volume is a measure of space (b) know what measurements are required to calculate volume, and how to obtain them (c) know that measurements must be in the same units before calculating volume (d) know that the volume of a cuboid = length x width x height (or depth) (e) know that area is measured in cubic units

If it has curved sides, a piece of string or cotton may be useful If it has curved sides, a piece of string or cotton may be useful. Go around the edge of the shape and then measure the length of the piece of thread.

Finding areas The area of a shape is the amount of surface that it covers. These shapes both have an area of 8 squares Tip: If the shape has curved sides, count all the squares that are bigger than a half

Areas of rectangles and shapes Finding the area of a rectangle is easy if you know the length and width: 4 cm 5 cm 3 cm Area = 4 x 4 cm = 16 cm2 Area = 3 x 5 = 15 cm2

To find the area of a shape that is made up from different rectangles joined together just find the area of each part and then add them together. 2 cm 4 cm Area of big rectangle is 4 x 2 = 8 cm2 Area of square is 2 x 2 cm = 4 cm2 Total area = 12 cm2

Find the area of each shape 2. = ___cm2 1. = ___cm2 4 cm 3 cm 4 cm 5 cm 3 cm 3. = ___cm2 2 cm 2 cm 3 cm 2 cm 6 cm

Other shapes Triangles have area = ½ x base x height. Parallelograms have area = base x height. Circles have area = π x radius x radius.

Volume Volume is a measure of the space taken up by a solid object and is measured in cubic units such as cm3 or cubic metres m3 A solid such as a cube or cuboid is three-dimensional (3D) which means you need three measurements to work out its volume, length, width and height. Each of these diagrams represents a shape made from unit cubes Volume = 8 cm3 Volume = 5 cm3

Each of these 2 cuboids has the same volume, 6 cm3 And the same dimensions: length 3cm width 2 cm, height 1 cm. The volume of the first can be found by counting the unit cubes. The volume of the second is found using the rule: Volume of a cuboid = length x width x height 3 x 2 x 1 = 6 cm3

Volume of a cube = length x length x length = length3 This cube has sides of length 2 cm Its volume is 2 x 2 x 2 = 8 cm3

The most important thing to remember when you are working out practical examples of volume is that all measurements must be in the same units. Example 1: 30cm 1 m 20 cm Ann's window box is a cuboid of length 1 m, width 20 cm and height 30 cm. Work out its volume. Make all the units in centimetres (1 m = 100 cm) so the volume is 100 x 20 x 30 = 60 000 cm3

Make all the units metres (10 cm = 0.1 m) so the volume = 8 x 2 x 0.1 Example 2: Igor is working out how many cubic metres of concrete he will need for his patio. It will be 2 metres wide and 8 metres long and he needs to make it 10 cm deep. How much concrete will he need? Make all the units metres (10 cm = 0.1 m) so the volume = 8 x 2 x 0.1 = 16 x 0.1 = 1.6 m3 10cm 8m 2 m

Example 3: Bonny has made a rectangular garden pond 2 m long and 1 m wide. She wants to fill it to a depth of 30 cm. How many litres of water will she need? Make all the units centimetres 200 x 100 x 30 = 600 000 cm3 Remember that 1 litre = 1000 cm3 600 000 1 000 = 600 She will need 600 litres of water

Volume of prisms A prism is a 3d object that has the same shape throughout. (In Maths speak – it has a uniform cross-section) Think about a tin of beans or a Toblerone.

Volume of prisms Now the volume of a cuboid is length x width x height But length x width = area So.... The volume of a cuboid is the same as area x height

Volume of prisms This rule works for ALL prisms... Volume = area of the cross-section x height 5cm 15cm The volume of this cylinder = area of the circle x height = π x 5 x 5 x 15 = 375 x π = 1178cm³

Volume = area of the cross-section x height Volume of prisms Volume = area of the cross-section x height The volume of this triangular prism = area of the triangle x height = ½ x 5 x 2 x 4 = ½ x 2 x 5 x 4 = 5 x 4 = 20cm³

Volume = area of the cross-section x height Volume of prisms Volume = area of the cross-section x height The volume of this L-shaped prism = area of the L x height Area of the L = (1 x 3) + (1 x 2) = 3 + 2 = 5cm² 1cm 2cm So the volume of the prism = 5 x 8 = 40cm³