Area · Grade 9
In Grade 9 you learn: sectors and composite shapes.
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 trapezium has an area of 36 cm² and parallel sides of 5 cm and 7 cm. Find its height.
Answer: 6 cm
Example 2
A circle has a radius of 5 cm. Find its area to 1 decimal place.
Answer: 78.5 cm²
Example 3
Find the area of a parallelogram with a base of 8 cm and a perpendicular height of 5 cm.
Answer: 40 cm²
Example 4
A trapezium has parallel sides of 7 cm and 11 cm and a height of 4 cm. Find its area.
Answer: 36 cm²
Example 5
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
Example 6
A rectangle has an area of 48 cm² and a perimeter of 28 cm. Find its length and width.
Answer: 8 cm, 6 cm