Discussion
The distance between two parallel sides of a trapezium is 8 cm. If the perimeter of the trapezium is 52 cm and its non-parallel sides are of length 10 cm each, then area of the trapezium (in cm2) is :
Answer: C
The area is 128 cm2.
The perimeter is the two parallel sides plus the two non-parallel sides, so the parallel sides together measure
\[ 52 - (10 + 10) = 32\ \text{cm} \]
The area of a trapezium is half the sum of the parallel sides times the distance between them:
\[ \begin{aligned} \text{Area} &= \tfrac{1}{2} \times 32 \times 8 \\ &= 128\ \text{cm}^{2} \end{aligned} \]
Forgetting the half doubles this to 256, which is not offered, and 64 is half the correct area. The individual lengths of the parallel sides are not needed, only their sum.
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