Question

Four equal circles, each of radius 5 cm, touch each other, as shown in the figure. Find the area included between them.

Answer 1

Radius = 5 cm
AB = BC = CD = AD = 10 cm
All sides are equal, so it is a square.
Area of a square = ${\mathrm{Side}}^2$
Area of the square = ${10}^2=100{\mathrm{cm}}^2$
Area of the quadrant of one circle = $\frac{1}{4}{\mathrm{\pi r}}^2$

$$\begin{gathered} =\frac{1}{4}\times \frac{22}{7}\times 5\times 5 \\ =19.64{\mathrm{cm}}^2 \end{gathered}$$
Area of the quadrants of four circles = $19.64\times 4=78.57{\mathrm{cm}}^2$
Area of the shaded portion = Area of the square $-$ Area of the quadrants of four circles
$$\begin{gathered} =100-78.57 \\ =21.43{\mathrm{cm}}^2 \end{gathered}$$