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Area is the amount of space taken up by a surface or 2-D shape. It is measured in squares with metric units mm², cm², m² and km².

Areas of rectangles, triangles, simple compound shapes and circles is covered in Geometry & measures - area

Calculate the areas of kites, parallelogram, rhombuses, trapeziums and compound shapes.

A parallelogram is a 2-D shape with 2 pairs of parallel sides.

When this triangle is moved from the left-hand side of the parallelogram to the right-hand side the area remains the same but shape is now a rectangle.

The area of a parallelogram is the same as the area of the rectangle.

Example

Calculate the area of this parallelogram.

Solution

Area of a parallelogram = base x perpendicular height

Area = 9 x 6 = 54 cm²

A kite is a 2-D shape with 2 pairs of equal sides. The diagonals cross at right angles.

When a rectangle is drawn around the kite with the length and width equal to the diagonals of the kite it is clear to see that the rectangle has twice the area of the kite.

Therefore, the area of a kite can be found by multiplying the two diagonals and then dividing the answer by two.

Area of Kite = length x width ÷ 2

Or multiply the diagonals and divide by 2

Example

Calculate the area of the kite.

Area of Kite = length x width ÷ 2
Or multiply the diagonals and divide by 2

The diagonals are 90 cm and 1.8 m
Firstly change 90 cm into metres.
90 cm = 0.9 m
Area = 1.8 x 0.9 ÷ 2 = 0.81 m²

A rhombus is both a parallelogram and a kite. The area can be calculated using either method.

Example

Calculate the area of the rhombus.

In this rhombus the base and the perpendicular height are known so the area is calculated using

Area of a parallelogram = base x perpendicular height

Area = 15 x 14.4 = 216 cm²

The same rhombus has the lengths of the diagonals known so the area is calculated by

multiply the diagonals and dividing by 2

Area = 24 x 18 ÷ 2 = 216 cm²

Some trapezia/trapeziums look a little different. Take care to identify the parallel sides before using the formula.

Example

Calculate the area of this trapezium.