Area · Grade 8
In Grade 8 you learn: area of circles and units of area.
Area is the amount of flat space a shape covers, measured in square units such as cm² and m². Count the squares, or use the formula for the shape; a compound shape splits into simpler shapes.
Key facts
- Triangle: area = ½ × base × perpendicular height.
- Parallelogram: area = base × perpendicular height.
- Trapezium: area = ½ × (a + b) × h, where a and b are the parallel sides.
Worked examples
Example 1
A triangle has a base of 10 cm and a perpendicular height of 7 cm. Find its area.
Answer: 35 cm²
Example 2
A lawn 12 m by 8 m has a path 1 m wide all round it. Find the area of the path.
Answer: 44 m²
Example 3
A trapezium has parallel sides of 6 cm and 10 cm and a height of 5 cm. Find its area.
Answer: 40 cm²
Example 4
A trapezium has an area of 36 cm² and parallel sides of 5 cm and 7 cm. Find its height.
Answer: 6 cm
Example 5
A circle has a radius of 5 cm. Find its area to 1 decimal place.
Answer: 78.5 cm²
Example 6
A right-angled triangle with shorter sides 4 cm and 3 cm is cut from a rectangle 12 cm by 5 cm. Find the area left.
Answer: 54 cm²