Question

Find the area of the shaded region in figure, if $AC=3$ cm, $BC=4$ cm and $O$ is the center of the circle.

• A. $1.071$ $c{m}^2$
• B. $3.821$ $c{m}^2$
• C. $3.071$ $c{m}^2$
• D. $4.071$ $c{m}^2$

Answer 1

Answer: (B)

$3.821$ $c{m}^2$

Given: $AC=3$ cm, $BC=4$ cm
In $\Delta ABC$,
$(AC{)}^2+(BC{)}^2=(AB{)}^2$
$3^2+4^2=(AB{)}^2$
$9+16=(AB{)}^2$
$(AB{)}^2=25$
$AB=5$ cm
Area of shaded region $=$ Area of semicircle or side $AB-$ Area of $\Delta ABC$
$=$ $\frac{\pi r^2}{2}-\frac{1}{2}\times AC\times BC$
$=$ $\frac{22}{7}\times \frac{{2.5}^2}{2}-\frac{1}{2}\times 3\times 4$ (Where $r=\frac{AB}{2}=\frac{5}{2}=2.5$)
$=$ $9.821-6$
$=3.821$
So, the area of the shaded region is $3.821$ $c{m}^2$