Discussion
The area of a trapezium is 105 cm2 and its height is 7 cm. If one of the parallel sides is longer than the other by 6 cm, then the length of the longer side, in cm, is
Answer: A
The longer parallel side is 18 cm.
Let the shorter parallel side be a cm, so the longer is a + 6. The area of a trapezium is half the sum of the parallel sides times the height:
\[ \begin{aligned} \tfrac{1}{2}(a + a + 6) \times 7 &= 105 \\ 2a + 6 &= 30 \\ a &= 12 \end{aligned} \]
The sides are 12 cm and 18 cm, and the longer is 18 cm. Check: \(\frac{1}{2}(12 + 18) \times 7 = 105\). 12 is the shorter side, the trap for anyone who stops at a, and 15 is the average of the two.
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