Question

Find the area of the shaded region in given Fig. where arcs drawn with centres $A,B,C$ and $D$ intersect in pairs at mid-points $P,Q,R$ and $S$ of the sides $AB,BC,CD$ and $DA$, respectively of a square $ABCD$ (Use $\pi =$3.14).

• A. $30.96$ $c{m}^2$
• B. $90.96$ $c{m}^2$
• C. $120.96$ $c{m}^2$
• D. $180.96$ $c{m}^2$

Answer 1

The correct option is A $30.96$ $c{m}^2$

Area of all four sectors made by square and circle are equal.

And each sector have an angle of ${90}^0$

And radius of circle is $\frac{12}{2}cm=6cm$

Area of shaded region $=$ Area of square $ABCD$ $-4\times$ Area of one sector

$\Rightarrow$ Area of shaded region $=$ Area of square $ABCD$ $-$ Area of circle with radius $6cm$

$=12\times 12-\pi \times 6^2{cm}^2$

$=144-113.04{cm}^2$

$=30.96{cm}^2$