Areas
Areas of Parallelograms, Trapeziums, Kites and Rhombuses

The formulae for calculating the areas of these shapes are:

Parallelogram
A = bh
Trapezium
A = (a + b)h
Kite
A = ab

The area of a rhombus can be found using either the formula for a kite or the formula for a parallelogram.

Worked Examples

1

Find the area of this kite.

Show me

Using the formula A = ab with a = 5 and b = 8 gives

A = × 5 × 8
= 20 cm²
2

Find the area of this shape.

Show me

The shape is made up of a parallelogram and a trapezium.

Area of parallelogram = 2 × 4
= 8 cm²
Area of trapezium = (8 + 12) × 3
= 30 cm²
Total area = 8 + 30
= 38 cm²

Exercises

Find the area of the shaded regions in the following figures.

(a)
m²
(b)
m²
(c)
cm²
(d)
cm²
(e)
cm²
(f)
m²
(g)
cm²
(h)
m²

The diagram shows the vertical side of a swimming pool.

(a)

Find the area of the side of the pool.

m²

The width of the swimming pool is 4 m.

(b)

Find the area of the rectangular end of the swimming pool.

m²
(c)

Find the area of the horizontal base of the pool.

m²
(d)

Find the total area of the sides, ends and horizontal base of the pool.

m²

In a car park, spaces are marked out in parallelograms.

Find the area of each parking space.

m²

A kite is cut out of a sheet of plastic as shown.

(a)

Find the area of the kite.

cm²
(b)

Find the area of the plastic that would be wasted.

cm²
(c)

Would you obtain proportionately similar results if you cut a kite out of a rectangle of plastic with dimensions 140 cm by 80 cm?

, because the area of the kite would be cm²
and the area of the waste would be cm²

Find the area of each of the following shapes.

(a)
cm²
(b)
cm²
(c)
cm²
(d)
cm²
(e)
cm²
(f)
cm²
(a)

Find the area of parallelogram ABCD.

cm²
(b)

Find the area of the triangle ABC.

cm²