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Length and Area

Units of Length | Area

Units of Length

On the metric system, we use the following units for length: millimetres (mm), centimetres (cm), metres (m) and kilometres (km).

10 mm = 1 cm
100 cm = 1 m
1 000 m = 1 km

Perimeter

This is the distance around the outside of a shape. To calculate the perimeter, we add together the lengths of the sides of the shape.

Example 1: Calculate the perimeter of the rectangle ABCD.

Perimeter = 15 + 15 + 8 + 8 = 46 cm

Note: If we use L for length and W for width, the perimeter (P) can be written as a formula:

P = 2L + 2W

Example 2: Calculate the perimeter (P) of the shape below.

P = 5 + 5 + 3 + 3 + 2 + 2 + 10 + 4 = 34 cm

Note: In this example we need to work out the length of 4 cm (10 – 6 = 4). The other missing lengths 2 cm and 5 cm can be found from the shape.

Area

Area is the space inside a shape. It is measured by dividing the shape into squares and counting them. If the squares' sides are 1 cm in length, then we can use the units cm².

Irregular shapes can be drawn on a grid and the area estimated by counting the squares. Parts of a square need to be added to make a whole square.

For example: Estimate the area of the shape below:

Area = 3½ squares

Regular shapes for example, triangles, rectangles and kites, have a formula for calculating the area.

Area of a rectangle

Area = Length x Width

For example: Calculate the volume of the cuboid shown below. Calculate the area of the rectangle ABCD.

Area = 15 x 8= 120 cm² (Note the units of area: cm² )

Area of a triangle

Area = ½ x Base x Height

For example: Calculate the area of triangle ABC.

Area = ½ x 10 x 6 = ½ x 60 = 30 cm²

(Note: 10 x 60 would give the area of the rectangle standing on BC, the area of the triangle is half this area).

Area of a parallelogram

Area = Base x Height

For example: Calculate the area of the parallelogram PQRS.

Area = 10 x 6 = 60 cm²

Area of a kite and rhombus

Area = ½ (the product of the diagonals)

For example: Calculate the areas of the kite ABCD and the rhombus LMNO.

Area of ABCD and LMNO = ½ x 10 x 6 =30 cm²

Area of a trapezium

Area = ½ (the sum of the parallel sides) x the height

For example: Calculate the area of the trapezium ABCD.

Area = ½ (10+20) x 5 = ½ x 30 x 5 = 75 cm²

Note: Sometimes the area is given in a problem and we are asked to calculate the length of one of the sides.

For example: Calculate the length of QR in the triangle, given that the area is 20 cm².

20 = ½ x 4 x QR
20 = 2 x QR
QR = 10 cm

Compound shapes

In some problems it is necessary to divide the shape into regular shapes. We can add or subtract areas.

For example: Calculate a) the total area and b) the shaded area in the diagram below.

a) Total area

= area A + area B
= (2 x 3) + (5 x 10)
= 6 + 50
= 56 cm²

b) Shaded area

= 56 – (2 x 2)
= 52 cm²