The area of a trapezium is 216 m
Question:

The area of a trapezium is 216 m2 and its height is 12 m. If one of the parallel sides is 14 m less than the other, find the length of each of the parallel sides.

Solution:

Let the length of the parallel sides be $\mathrm{x} \mathrm{m}$ and $(x-14) \mathrm{m}$.

Then, area of the trapezium $=\left\{\frac{1}{2} \times(x+x-14) \times 12\right\} \mathrm{m}^{2}$

$=6(2 x-14) m^{2}$

$=(12 x-84) m^{2}$

But it is given that the area of the trapezium is $216 \mathrm{~m}^{2} .$

$\therefore 12 x-84=216$

$\Rightarrow 12 x=(216+84)$

$\Rightarrow 12 x=300$

$\Rightarrow x=\frac{300}{12}$

$\Rightarrow x=25$ Hence, the length of the parallel sides are $25 \mathrm{~m}$ and $(25-14) \mathrm{m}$, which is equal to $11 \mathrm{~m} .$