Question

In the fig., the outer trapezium $ABCD$ has area $320c{m}^2$. The area of the shaded region is $140c{m}^2$. Find the area of the inner trapezium $EFGH$. If the length of the parallel sides of the inner trapezium are $16cmand20cm$, find height $h$.

• A. $180c{m}^2,h=5cm$
• B. $180c{m}^2,h=10cm$
• C. $170c{m}^2,h=10cm$
• D. $180c{m}^2,h=12cm$

Answer 1

The correct option is B $180c{m}^2,h=10cm$

Area of $EFGH$ $=$ ar $ABCD$ - $140$ ${cm}^2$

$\Rightarrow \frac{1}{2}\times (16+20)\times h=320-140\Rightarrow 18h=180\Rightarrow h=$10$cm$

$\therefore$ Area of $EFGH$ $=$ $320-140$ $=$ $180$${cm}^2$