Two parallel sides of a trapezium are 29 cm and 21 cm. Non-parallel sides are equal and each is of length 8.5 cm. What is the area of the trapezium?

Explanation

Dropping perpendiculars from the shorter parallel side to the longer one creates two identical right triangles with bases \frac{29-21}{2} = 4\text{ cm}. The height h = \sqrt{8.5^2 - 4^2} = \sqrt{72.25 - 16} = 7.5\text{ cm}. The area is \frac{1}{2}(29+21) \times 7.5 = 25 \times 7.5 = 187.5\text{ cm}^2.

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