Question

The area of a trapezium is $300m^2$. The perpendicular distance between the two parallel sides is $15m$. If the difference of the parallel side is $16m$, find the length of the parallel sides.

Answer 1

Area of trapezium is given by

$A=\frac{1}{2}(a+b)h$

If one side is $a$ then the other side is $a-16$ since the difference of parallel sides is $16$

$\therefore$ A $=\frac{1}{2}(a+a-16)\times 15=300$

$\Rightarrow \frac{1}{2}(2a-16)\times 15=300$

$\Rightarrow (2a-16)\times 15=600$

$\Rightarrow (2a-16)=40$ [By dividing both side by 15]

$2a=56$

$a=28m$

The other parallel side$=a-16$

$a-16=28-16=12$

Therefore, the sides are $28m$ and $12m.$