Question

Four equal circles, each of radius $5$ cm touch each other. Find the area included between them (Take $\pi$ $=3.14$).

Answer 1

Let the side of square is $a$.

$\therefore$ $a=5+5=10cm$

$\Rightarrow$ Area of square $=a^2=(10{)}^2=100c{m}^2$

$\Rightarrow$ $r=5cm$

$\Rightarrow$ Area of circle $=\pi r^2=3014\times (5{)}^2=78.5c{m}^2$

$\Rightarrow$ Area of quadrant inside square $=\frac{1}{4}\pi r^2=\frac{1}{4}\times 78.5cm$

$\Rightarrow$ Area of shaded region = Area of square - $4\times$ Area of quadrant.

$\therefore$ Area of shaded region $=100-4\times \frac{1}{4}\times 78.5$

$\therefore$ Area of shaded region $=100-78.5=21.5c{m}^2$