iGCSE Mathematics (0580) :E5.2 Carry out calculations involving the perimeter and area.iGCSE Style Questions Paper 2

Question

The diagram shows some land in the shape of a triangle ABC.
Houses are built on this land.
Each house requires 400 m² of land.

Find the greatest number of houses that can be built on this land.

▶️ Answer/Explanation

Solution

Ans: 1150

First calculate triangle area: ½ × 800 × 2300 × sin30°

sin30° = 0.5, so area = ½ × 800 × 2300 × 0.5 = 460,000 m²

Number of houses = Total area ÷ Area per house

460,000 ÷ 400 = 1,150 houses

Question

The diagram shows a trapezium.

The area of the trapezium is \(42cm^{2}\)

Calculate the value of x.

▶️ Answer/Explanation

Solution

Ans: 4.5

Area of trapezium = ½ × (sum of parallel sides) × height

42 = ½ × (9.5 + x) × 6

42 = 3 × (9.5 + x)

14 = 9.5 + x

x = 4.5 cm

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