Question

The area of a trapezium with equal non-parallel sides is $168m^2$. If the lengths of the parallel sides are $36m$ and $20m$, then find the length of the non-parallel sides.

Answer 1

Length of the parallel sides are $36m$ and $20m$.
Area of trapezium $=168m^2$
$\because$ Area of a trapezium $=\frac{1}{2}\times [\text{Sum of parallel sides]}\times \text{Height}$
$\therefore 168=\frac{1}{2}\times [36+20]\times \text{Height}\Rightarrow \text{Height}=\frac{168\times 2}{56}=\frac{336}{56}=6m$

In $\Delta ACB$, using Pythagoras theorem,
$(AB{)}^2=(BC{)}^2+(AC{)}^2\Rightarrow (AB{)}^2=(8{)}^2+(6{)}^2\Rightarrow (AB{)}^2=64+36\Rightarrow (AB{)}^2=100\therefore AB=\sqrt{100}=10m$
Hence, the length of the non-parallel side is 10 m.