Question

In the given figure, $ABC$ is a quadrant of a circle of radius $14cm$ and a semicircle is drawn with $BC$ as diameter. Find the area of the shade region.

• A. $98c{m}^2$
• B. $38c{m}^2$
• C. $48c{m}^2$
• D. $58c{m}^2$

Answer 1

The correct option is A $98c{m}^2$

Area of shaded region=area of semicircle of diameter BC-{area of quadrant of radius AB/AC- area of $△$ABC}

$\because$ BC is hypotenuse of right angle $△ABC$

here $AB=BC=14$

So, $BC=14\sqrt{2}=2\times radius\Rightarrow radius=7\sqrt{2}$

So, Area of semicircle of diameter BC$=\frac{\pi r^2}{2}$

$=\frac{1}{2}\times \frac{22}{7}\times (7\sqrt{2}{)}^2$

$=154c{m}^2$

Area of quadrant of radius AB/AC$=\frac{\pi r^2}{4}$

$=\frac{1}{4}\times \frac{22}{7}\times 14\times 14$

$=154c{m}^2$

Area of $△ABC=\frac{1}{2}\times h\times b$

$=\frac{1}{2}\times 14\times 14=98c{m}^2$

Now, area of shaded region$=154-\{154-98\}=98c{m}^2$

Hence, area of shaded region$=98c{m}^2$