Question

A paper is in the form of a rectangle ABCD in which $AB=30cm$ and $DA=20cm$. A semicircular portion with BC as the diameter is cut off. Find the area of the remaining part.

Answer 1

We have, $AB=CD=30cm$ and $AD=BC=20cm$

Since, $ABCD$ is a rectangle and semicircular portion with $BC$ diameter is cut off. it means the radius of the semicircle is $10cm$.

Therefore, the area of remaining part is

= Area of rectangle - Area of semicircle

$=length\times breadth-\frac{\pi r^2}{2}$

$=AB\times AD-\frac{\pi \times (\frac{BC}{2}{)}^2}{2}$

$=30\times 20-\frac{\pi \times (\frac{20}{2}{)}^2}{2}$

$=600-\frac{\pi \times (10{)}^2}{2}$

$=600-\frac{\pi \times 100}{2}$

$=600-3.14\times 50$

$=600-157$

$=443c{m}^2$