Area and perimeter: solved examples

Worked examples of area and perimeter, from easy to hard, with every step written out. Try each one yourself first, then check the working.

✓ Every answer here is computed and checked by the math engine

Easy

Example 1. A rectangle is 12 cm long and 7 cm wide. What is its perimeter in cm?
1. Add the four sides. $2 \times (12 + 7) = 38\ \text{cm}$
Answer: $38\ \text{cm}$
Example 2. A rectangle is 2 cm long and 7 cm wide. What is its area in cm²?
1. Multiply length by width. $2 \times 7 = 14\ \text{cm}^2$
Answer: $14\ \text{cm}^2$
Example 3. A rectangle is 16 cm long and 19 cm wide. What is its area in cm²?
1. Multiply length by width. $16 \times 19 = 304\ \text{cm}^2$
Answer: $304\ \text{cm}^2$

Example 4. A parallelogram has a base of 12 cm and a perpendicular height of 7 cm. What is its area in cm²?
1. Multiply base by height. $12 \times 7 = 84$
Answer: $84\ \text{cm}^2$
Example 5. A triangle has a base of 2 cm and a perpendicular height of 7 cm. What is its area in cm²?
1. Halve base × height. $\tfrac{1}{2} \times 2 \times 7 = 7$
Answer: $7\ \text{cm}^2$
Example 6. A triangle has a base of 16 cm and a perpendicular height of 19 cm. What is its area in cm²?
1. Halve base × height. $\tfrac{1}{2} \times 16 \times 19 = 152$
Answer: $152\ \text{cm}^2$

Example 7. A trapezium has parallel sides of 9 cm and 13 cm and a height of 15 cm. What is its area in cm²?
1. Average the parallel sides and multiply by the height. $\tfrac{1}{2} \times (9 + 13) \times 15 = 165$
Answer: $165\ \text{cm}^2$
Example 8. A trapezium has parallel sides of 2 cm and 7 cm and a height of 3 cm. What is its area in cm²?
1. Average the parallel sides and multiply by the height. $\tfrac{1}{2} \times (2 + 7) \times 3 = \frac{27}{2}$
Answer: $\frac{27}{2}\ \text{cm}^2$
Example 9. A trapezium has parallel sides of 13 cm and 20 cm and a height of 2 cm. What is its area in cm²?
1. Average the parallel sides and multiply by the height. $\tfrac{1}{2} \times (13 + 20) \times 2 = 33$
Answer: $33\ \text{cm}^2$

Practise with fresh questions of the same kind. You get hints, the full working and instant checking.