## Area Area is the amount of space taken up by a surface.

The areas and perimeters of simple figures such as squares and rectangles can be calculated using formulae.

The perimeter of a shape is the total length of all of its sides. Perimeters are measured using the units of length, i.e. metres.

### Units of Area

There are two basic units for measuring area:

• A square metre is the area occupied by a square with each side 1 metre long. It is written as 1 m2.
• An are is the area occupied by a square of length 10 m.

Other common units for area are:

 Unit Symbol Units for measuring: Conversion Square centimetre cm2 Paper, material 10 000 cm2 = 1 m2 Square kilometres km2 Area of countries 1 km2 = 106 m2 Hectare ha Land area, e.g. farms 1 ha = 10 000 m2 A 100 m by 100 m square

### Area and Perimeter Formulae

 Shape Name Perimeter Area Square P= 4 × l = 4 l A = length × width = l × l = l 2 Rectangle P = 2b + 2h A = base × height = b × h = bh h is the perpendicular height. Triangle P = a + b + c A= 1⁄2 × base × height =1⁄2 × b × h =1⁄2bh h is the perpendicular height. Parallelogram P = 2b + 2a A = base x height = bh h is the perpendicular height. Rhombus P = Sum of all sides = 4b A = base × height = b × h or A = 1⁄2 × (product of length of diagonals) h is the perpendicular height. Trapezium P = Sum of all sides A = 1⁄2 × ( a + b ) × h

### Composite Shapes

Not all shapes are like the ones shown in the table. Some shapes are combinations of those shown above.

To find the areas of composite shapes, break the shape up into squares, rectangles, triangles etc.

e.g. Find the shaded area The shaded area is made up of a shaded rectangle and triangle less the white rectangle. Shaded area = 10 × 5 + 0.5 × 5 × 6 − 7 × 2 = 50 + 15 − 14 = 51 m2

### Irregular Areas

Many shapes are not regular or composite. The only way to calculate the area of this type of shape is to make approximations.

e.g. The area of an island could be estimated by placing a map of the island on a grid of squares and counting the number of full and part squares. Number of squares on island is about 24 Area of island = 24 km2 (approx.)