In figure, AB is a diameter of the circle, AC = 6 cm and BC = 8 cm. Find the area of the shaded region, (use π = 3.14)
Given, AC = 6 cm and BC = 8 cm
We know that, triangle in a semi-circle with hypotenuse as diameter is right angled triangle.
$\therefore \quad \angle C=90^{\circ}$
In right angled $\triangle A C B$, use Pythagoras theorem,
$\therefore$ $A B^{2}=A C^{2}+C B^{2}$
$\Rightarrow \quad A B^{2}=100$
$\Rightarrow \quad A B=10 \mathrm{~cm} \quad$ [since, side cannot be negative]
$\therefore$ Area of $\triangle A B C=\frac{1}{2} \times B C \times A C=\frac{1}{2} \times 8 \times 6=24 \mathrm{~cm}^{2}$
Here, diameter of circle, $A B=10 \mathrm{~cm}$
$\therefore \quad$ Radius of circle, $r=\frac{10}{2}=5 \mathrm{~cm}$
Area of circle $=\pi r^{2}=3.14 \times(5)^{2}$
$=3.14 \times 25=78.5 \mathrm{~cm}^{2}$
Area of the shaded region $=$ Area of circle $-$ Area of $\triangle A B C$
$=78.5-24=54.5 \mathrm{~cm}^{2}$
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