Perimeter and area of basic shapes
Perimeter and area
- Perimeter = the distance all the way round. Area = the flat space inside.
- $b$ is the base, $h$ the perpendicular height.
| Shape | Area |
|---|---|
| rectangle | length $\times$ width |
| triangle | $\tfrac12 \times b \times h$ |
| parallelogram | $b \times h$ |
| trapezium | $\tfrac12(a+b)h$ |
Practice
A triangle has base 10 cm and height 6 cm. Find its area (cm²).
½ × 10 × 6 = 30 cm².
Practice
A rectangle is 8 cm by 5 cm. Find its perimeter (cm).
Perimeter = 2(8 + 5) = 26 cm.
Worked example
- A trapezium has parallel sides $6\ \text{cm}$ and $10\ \text{cm}$, height $4\ \text{cm}$.
- Area $= \tfrac12(6+10)\times 4 = \tfrac12 \times 16 \times 4 = 32\ \text{cm}^2$.
Practice
A trapezium has parallel sides 6 cm and 10 cm and height 4 cm. Find its area (cm²).
½(6 + 10) × 4 = ½ × 16 × 4 = 32 cm².
You've got it
Key idea
- rectangle area = length $\times$ width; triangle $= \tfrac12 b h$
- parallelogram $= bh$; trapezium $= \tfrac12(a+b)h$
- $h$ is always the perpendicular height