Stage 11 · Shape & space
Area (II)
Base × height; a triangle's is half that.
How to do it
Method
Base × height; a triangle's is half that
Base 8, height 5: 8 ÷ 2 = 4, 4 × 5 = 20
Another way
Base × height ÷ 2
8 × 5 = 40, 40 ÷ 2 = 20
In full
First find the base and its height: the height is at right angles to the base, and a slanting side's length is not the height. A parallelogram's area = base × height; a triangle's is half that of the parallelogram with the same base and height: base × height ÷ 2; a trapezium's = (top + bottom) × height ÷ 2. A triangle with base 8 cm and height 5 cm: 8 × 5 = 40, 40 ÷ 2 = 20, so 20 cm². Quicker: halve the even number first, so the numbers stay small: 8 ÷ 2 = 4, 4 × 5 = 20 — the same answer. A trapezium with top 3 cm, bottom 7 cm and height 4 cm: 3 + 7 = 10, 10 × 4 = 40, 40 ÷ 2 = 20 cm². Cutting and rearranging the shapes into rectangles or parallelograms shows where these formulas come from.
Worked examples
Have a go first, then open each one for the answer and the working.
Example 1
Area of the parallelogram = ? cm²
Show the answer and working
Answer: Area of the parallelogram = 77 cm²
A parallelogram's area is base × height: 7 × 11 = 77, so 77 cm²
Example 2
Area of the triangle = ? cm²
Show the answer and working
Answer: Area of the triangle = 14 cm²
A triangle's area is base × height ÷ 2: 4 ÷ 2 = 2, 7 × 2 = 14, so 14 cm²
Example 3
Area of the parallelogram = ? cm²
Show the answer and working
Answer: Area of the parallelogram = 96 cm²
A parallelogram's area is base × height (the slanting 10 cm side is not the height): 12 × 8 = 96, so 96 cm²
Example 4
Area of the trapezium = ? cm²
Show the answer and working
Answer: Area of the trapezium = 55 cm²
A trapezium's area is (top + bottom) × height ÷ 2: 3 + 8 = 11, 10 ÷ 2 = 5, 11 × 5 = 55, so 55 cm²
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