figure: ar-a3-three.png Three circles, each of radius 7 cm, touch each other…

Step 1. The triangle of centres. Its side is $7 + 7 = 14\ \text{cm}$. Its area is $\dfrac{\sqrt{3}}{4} \times 14^2 = 49\sqrt{3}\ \text{cm}^2$, which is $84.77\ \text{cm}^2$.

Step 2. The sectors. Each angle of the triangle is $60^\circ$, so each sector is $\dfrac{1}{6}$ of a circle. Three of them make half a circle: $\dfrac{1}{2} \times \dfrac{22}{7} \times 49 = 77\ \text{cm}^2$.

Step 3. The difference. $84.77 - 77 = 7.77\ \text{cm}^2$.