year 8 maths

136 Chapter 3 Measurement and Pythagoras’ theorem
3D Area of special quadrilaterals
The formulas for the area of a rectangle and a triangle can be used to develop the area of other special
quadrilaterals. These quadrilaterals include the parallelogram, the rhombus, the kite and the trapezium.
Knowing the formulas for the area of these shapes can save a lot of time by dividing shapes into
rectangles and triangles.
Let’s start: Developing formulas
These diagrams contain clues as to how you might find the area of the shape using only what you know
about rectangles and triangles. Can you explain what each diagram is trying to tell you?
• Parallelogram • Rhombus
• Kite • Trapezium
1
2
h
Key ideas
■ Area of a parallelogram
Area = base × perpendicular height
or A = bh
■ Area of a rhombus and the area of a kite
b
y
Area = 1 × diagonal x × diagonal y
2
or A = 1 2 xy
x
y
x
■ Area of a trapezium
Area = 1 × sum of parallel sides × perpendicular height
2
h
b
h
or A = 1 h(a + b)
2
a
Cambridge Maths NSW
Stage 4 Year 8 Second edition
ISBN 978-1-108-46627-1 © Palmer et al. 2018
Cambridge University Press
Photocopying is restricted under law and this material must not be transferred to another party.