Question

A sheet of paper is in the from of rectangular ABCD in which $AB=40cm$ and $AD=28cm$. A semi-circular portion with BC as diameter is cut off. Find the area of the remaining paper.

Answer 1

$\Rightarrow$ $Diameter=BC=28cm$ [ Opposite sides of rectangle are equal ]

$\Rightarrow$ $Radius\left(r\right)=\frac{28}{2}=14cm$

$\Rightarrow$ Area of a semi-circle $=\frac{\pi r^2}{2}$

$\therefore$ Area of a semi-circle $=\frac{1}{2}\times \frac{22}{7}\times (14{)}^2=308c{m}^2$

$\Rightarrow$ Now, area of a sheet $=40\times 28=1120c{m}^2$

$\therefore$ Area of remaining paper $=$Area of sheet - Area of a semi circle.

$\Rightarrow$ Area of remaining paper $=1120c{m}^2-308c{m}^2=812c{m}^2$