Question

A rectangular piece is $20$ m long and $15$ m wide. Form its four corners, quadrants of radii $3.5$ m have been cut. Find the area of the remaining part.

Answer 1

$\Rightarrow$ Here, $l=20m,b=15cm,r=3.5m$ and $\theta ={90}^o$

$\Rightarrow$ Area of rectangle $=l\times b=(20\times 15)m^2=300m^2$

$\Rightarrow$ Area of a quadrant $=\frac{\theta }{{360}^o}\times \pi r^2$

$\Rightarrow$ Area of a quadrant $=\frac{{90}^o}{{360}^o}\times \frac{22}{7}\times 3.5\times 3.5$

$\therefore$ Area of a quadrant $=9.625m^2$

$\Rightarrow$ Area of $4$ quadrant $=4\times 9.625=38.5m^2$

$\Rightarrow$ Area of remaining part = Area of rectangle - Area of 4 quadrant

$\therefore$ Area of remaining part $=(300-38.5)m^2=261.5m^2$