Question

Four equal circles, each of radius ${}^{\prime }{a}^{\prime }$, touch one another. Find the area between them.

Answer 1

Area of shaded region $=$ Area of square $-4\times$ area of each quadrant

$={\left(2a\right)}^2-4\times \frac{1}{4}\times \pi \times a^2$

$={4a}^2-a^2\pi$

$=a^2(4-\pi )$

$=a^2(4-\frac{22}{7})$

$=\frac{6a^2}{7}$