Question

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

Answer 1

Given Area of Trapezium$=182c{m}^2,h=14cm$

Let the upper parallel side be $x$

other side $=x+16$ cm

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

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

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

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

$\Rightarrow (x+8)=\frac{182}{14}=13$

$\Rightarrow x=13-8=5$

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