**Question:**

In Fig. 20.38, a parallelogram is drawn in a trapezium, the area of the parallelogram is 80 cm2, find the area of the trapezium.

**Solution:**

The given figure is:

From above figure, it is clear that the length of the parallel sides of the trapezium are $22 \mathrm{~cm}$ and $10 \mathrm{~cm}$.

Also, it is given that the area of the parallelogram is $80 \mathrm{~cm}^{2}$ and its base is $10 \mathrm{~cm}$.

We know:

Area of parallelogram $=$ Base $\times$ Height

$\therefore 80=10 \times$ Height

Height $=\frac{80}{10}=8 \mathrm{~cm}$

So, now we have the distance between the parallel sides of trapezium, which is equal to $8 \mathrm{~cm}$.

$\therefore$ Area of trapezium $=\frac{1}{2} \times($ Sum of the parallel sides $) \times($ Distance between the parallel sides $)$

$=\frac{1}{2} \times(22+10) \times(8)$

$=128 \mathrm{~cm}^{2}$