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Year 8 Mathematics · Area of triangles and parallelograms

Name: ______________________

Date: ____________

1. A triangle has a base of 8 cm and a perpendicular height of 5 cm. What is its area?
- ☐ (a) 40 cm²
- ☐ (b) 20 cm²
- ☐ (c) 13 cm²
- ☐ (d) 26 cm²
2. A parallelogram has a base of 9 m, a slanted side of 5 m and a perpendicular height of 4 m. What is its area?
- ☐ (a) 45 m²
- ☐ (b) 20 m²
- ☐ (c) 36 m²
- ☐ (d) 26 m²
3. Which formula gives the area of a triangle?
- ☐ (a) A = b × h
- ☐ (b) A = 2 × (b + h)
- ☐ (c) A = b + h
- ☐ (d) A = ½ × b × h
4. How many square centimetres are in 1 square metre?
- ☐ (a) 10 000 cm²
- ☐ (b) 100 cm²
- ☐ (c) 1000 cm²
- ☐ (d) 1 000 000 cm²
5. A triangular garden bed has a base of 14 m and a perpendicular height of 9 m. What is its area in square metres?
6. A rectangular rug is 2.5 m long and 4 m wide. What is its area in square metres?
7. A triangle has an area of 24 cm² and a base of 8 cm. What is its perpendicular height in centimetres?
8. A rectangular wall is 5 m wide and 3 m high. One tin of paint covers 5 m². How many tins are needed for one coat?

Answer sheet

1. 20 cm² — A = ½ × 8 × 5 = ½ × 40 = 20 cm².
2. 36 m² — A = b × h = 9 × 4 = 36 m². The slanted side is not used.
3. A = ½ × b × h — A triangle is half of a parallelogram with the same base and height, so A = ½ × b × h.
4. 10 000 cm² — 1 m = 100 cm, so a 1 m square is 100 cm × 100 cm = 10 000 cm².
5. 63 m² — A = ½ × 14 × 9 = 7 × 9 = 63 m².
6. 10 m² — A = 2.5 × 4 = 10 m².
7. 6 cm — 24 = ½ × 8 × h, so 24 = 4 × h, which gives h = 6 cm.
8. 3 — Area = 5 × 3 = 15 m². 15 ÷ 5 = 3 tins.