BestMaths Online

Area of Polygons

The area of a polygon, such as a rectangle, is the amount of space enclosed by the polygon.

Units

The units used for measuring areas depends on the units used for measuring the length of the shape.

A square metre is the area occupied by a square with each side 1 metre long. It is written as 1 m².

A hectare is the area enclosed by a square with sides of length 100 metres

Other common units for area are:

Unit	Symbol	Units for measuring:
Square centimetre	cm2	Small shapes
Square kilometres	km2	Large areas such as the area of countries
Hectare	ha	Land area, e.g. farms

Converting between units

To convert between units of area is sometimes confusing. A diagram often helps.

e.g.

Convert 1 m2 into cm2.

From the diagram 1 m2 = 100 × 100 cm2 = 10 000 cm2

Area Formulae

Shape	Name	Area
	Square	A = length × width = l2
	Rectangle	A = base × height = b × h = bh
	Triangle	A = half × base × height   = 1⁄2 × b × h
	Parallelogram	A = base × height = bh
	Rhombus	A = base × height  = b × h  or  A = 1⁄2 × (product of length of diagonals)
	Trapezium	A = 1⁄2 × ( a + b ) ×  h

Composite Shapes

Composite shapes are shapes made up of shapes such as squares rectangles, semicircles etc.

To find out the area of composite shapes, break the larger shape up into smaller ones for which you can find the area.

Example

Note: The shape could have been broken up into two different rectangles using a vertical line.

The problem could also have been done by calculating the area of the larger rectangle and subtracting the corner that is missing.

Area of shape = 10 × 12 − 4 × 7
= 120 − 28
= 92 cm²