In given figure, semicircles have been drawn on all the sides of a right-angled triangle as shown.

Show that Area (A) + Area (B) = Area (C).

Right-angled triangle with legs $a$, $b$ and hypotenuse $c$: $a^2 + b^2 = c^2$

Semicircle A on leg $a$: area = $\left(\frac{1}{2}\right)\pi\left(\frac{a}{2}\right)^2 = \frac{\pi a^2}{8}$

Semicircle B on leg $b$: area = $\frac{\pi b^2}{8}$

Semicircle C on hypotenuse $c$: area = $\frac{\pi c^2}{8}$

$$\text{Area}(A) + \text{Area}(B) = \frac{\pi a^2}{8} + \frac{\pi b^2}{8}$$

$$= \frac{\pi(a^2 + b^2)}{8} = \frac{\pi c^2}{8} = \text{Area}(C).$$

Hence, proved.