Question

A parallelogram is drawn in a trapezium, the area of the parallelogram is $80c{m}^2$, find the area of the trapezium.

Answer 1

The given figure is:

From above figure,

Length of the parallel sides of the trapezium are $22cm$ and $10cm$.

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

We know that Area of parallelogram $=$ Base $\times$ Height

$\Rightarrow 80c{m}^2=10cm\times$ Height

Height $=\frac{80c{m}^2}{10cm}=8cm$

Therefore, height of the trapezium (Distance between the parallel sides) is $8cm$.

Now, Area of trapezium

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

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

$=32cm\times 4cm$

$=128c{m}^2$

Therefore, Area of the trapezium is $128c{m}^2$.