Question

Find the area of the shaded region in the figure, if $AB=5cm,AC=12cm$ and $O$ is the centre of the circle

Answer 1

Solution: Here, OR is the hypotenuse of $△ABC$,
because lines from two ends of diameter always make a right angle when they meet at circumference.
So, $B{C}^2=A{B}^2+A{C}^2$
$5^2+{12}^2$
= $25+144$ = $169$
= $BC$ = $13$
= Or, BC = $13cm$ Or radius = $6.5cm$
Area of triangle = $\frac{1}{2}$ x base x height
= $\frac{1}{2}$ x $12$ x $5$
= $6$ x $5$
$30$ sq cm
Area of semicircle = $\frac{1}{2}$ x $\pi$ $r^2$
= $\frac{1}{2}$ x $\pi$ x ${6.5}^2$
= $\frac{1}{2}$ x $3.14$ x $42.25$
= $\frac{132.665}{2}$
= $132.665$ sq. cm
area of shaded region = $132.665$ - $30$ = $102.665$ sq. cm