Question

Find the area of the segments shaded in figure, if CB = 12 cm, AC = 5 cm, and AB is the diameter of the circle with centre 'O' (Take $\pi$ = $\frac{22}{7}$).

• A. 36.39 ${cm}^2$
• B. 48.32 ${cm}^2$
• C. 56.54 ${cm}^2$
• D. 64 ${cm}^2$

Answer 1

The correct option is A 36.39 ${cm}^2$

Given: $\angle$ACB = ${90}^{\circ }$
So, using Pythagoras Theorem in right-angled $△$ ACB

$\therefore$ ${AB}^2$ = ${AC}^2$ + ${BC}^2$
$\Rightarrow$ ${AB}^2$ = $5^2$ + ${12}^2$ = 25 + 144
$\Rightarrow$ AB = $\sqrt{169}$
$\Rightarrow$ AB = 13 cm
Now, radius of circle = $\frac{1}{2}$$\times$ AB
= $\frac{1}{2}$$\times$ 13 = 6.5 cm
Now,
Area of semicircle OBCA = $\frac{1}{2}$$\times$$\pi$$r^2$
= $\frac{1}{2}$$\times$$\frac{22}{7}$$\times$${6.5}^2$
= 66.39 ${cm}^2$

Now, Area of $△$ ACB = $\frac{1}{2}$$\times$ AC$\times$ CB

= $\frac{1}{2}$$\times$ 5$\times$ 12
= 30 ${cm}^2$

Then,
Area of Shaded segment = (Area of semicircle OBCA - Area of $△$ ACB)

Area of Shaded segment = (66.39 - 30) ${cm}^2$ = 36.39 ${cm}^2$