A homeowner is having new wooden decking installed in her back garden. The decking area is shaped like a trapezium, with parallel sides of \(5.2\) m and \(8...
Question 1 Report
A homeowner is having new wooden decking installed in her back garden. The decking area is shaped like a trapezium, with parallel sides of \(5.2\) m and \(8.4\) m, and a perpendicular height between them of \(3.5\) m.
- Work out the area of the decking. (2)
- Decking boards cost \(£24\) per square metre. Work out the total cost of the decking. (2)
Answer Details
The area of a trapezium is found using \(\frac{1}{2} \times (\text{sum of parallel sides}) \times (\text{perpendicular height})\), and this area can then be used to find a real-world cost by multiplying by a price per square metre.
(a) With parallel sides 5.2 m and 8.4 m and height 3.5 m:
\[ \text{Area} = \frac{1}{2} \times (5.2 + 8.4) \times 3.5 = \frac{1}{2} \times 13.6 \times 3.5 = 23.8 \text{ m}^2 \][2]
(b) Total cost of the decking:
\[ 23.8 \times £24 = £571.20 \][2]
The height used in the trapezium formula must be the perpendicular distance between the two parallel sides, not the length of a slanted edge, since only the perpendicular height gives the correct area.
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