Question

In the figure, $ABCD$ is a square with side $10$. $BFD$ is an arc of a circle with centre $C$. $BGD$ is an arc of a-circle with centre $A$. What is the area of the shaded region?

• A. $100-50\pi$
• B. $100-257\pi$
• C. $50\pi -100$
• D. $25\pi -100$

Answer 1

The correct option is C $50\pi -100$

Length of Arc $BGD=$ Length of arc $BFD$

Since $AB=BC=10$

Construction: Join $BD$

As the given figure is a square, so area of $\Delta ABD=$ Area of $\Delta BCD$
and Area of Quadrant $ABGD=$ Area of Quadrant $BCDF$

Now, area of shaded region $=2($Area of Quadrant $ABGD-$ Area of $\Delta ABD)$
$A=2(\frac{\pi r^2}{4}-\frac{1}{2}\times b\times h)$
Here, $r=10,b=h=10$

Therefore, $A=2(25\pi -50)$
So, area of shaded region $=50\pi -100$.