A triangular flower bed in a garden has a base of 3.6 m and a perpendicular height of 2 m, as shown in the diagram. The gardener wants to cover the bed with...
Question 1 Report
A triangular flower bed in a garden has a base of 3.6 m and a perpendicular height of 2 m, as shown in the diagram. The gardener wants to cover the bed with fresh topsoil that costs £4.50 per square metre. He is comparing suppliers for the best price.
- Work out the area of the flower bed. (3)
- Work out the cost of the topsoil needed to cover the bed. (2)
Answer Details
The flower bed is a triangle, so its area is \( \dfrac{1}{2} \times \text{base} \times \text{height} \); once the area is known, multiplying by the cost per square metre gives the total cost of covering it.
- With base 3.6 m and perpendicular height 2 m:\[ \text{Area} = \frac{1}{2} \times 3.6 \times 2 = 3.6 \text{ m}^2 \][3] (1 for \(\frac{1}{2} \times 3.6\), 1 for multiplying by 2, 1 for 3.6 m\(^2\))
- Multiplying the area by the price of 4.50 per square metre:\[ \text{Cost} = 3.6 \times 4.50 = \pounds 16.20 \][2] (1 for \(3.6 \times 4.50\), 1 for \(\pounds 16.20\))
The perpendicular height, the dashed line shown at right angles to the base in the diagram, is what must be used in the triangle area formula; a slanted side of the triangle is never the correct height to substitute.
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