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Question

The area of a trapezium is $$182cm^2$$. Its height is $$14cm$$. The larger parallel side is longer than the other by $$16cm$$. Find the length of the parallel sides.


Solution

Given Area of Trapezium$$=182cm^2,h=14cm$$

Let the upper parallel side be $$x$$

other side $$=x+16$$ cm

Area of Trapezium $$=\dfrac{1}{2}h\left(a+b\right)$$ where $$a$$ and $$b$$ are the parallel sides

$$\therefore 182=\dfrac{1}{2}\times 14\left(x+x+16\right)$$

$$\Rightarrow 182=7\left(2x+16\right)$$

$$\Rightarrow 182=14\left(x+8\right)$$

$$\Rightarrow \left(x+8\right)=\dfrac{182}{14}=13$$

$$\Rightarrow x=13-8=5$$

$$\therefore$$ the shorter parallel side$$=5$$cm and the base of the Trapezium $$=5+16=21$$cm

Mathematics

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