Question:
Find the area of the shaded region in figure, where arcs drawn with centres A, B, C and D intersect in pairs at mid-point P, Q, R and 5 of the sides AB,
BC, CD and DA, respectively of a square ABCD. (use π = 3.14)
Solution:
Given, side of a square BC = 12 cm
Since, Q is a mid-point of BC
$\therefore$ Radius $=B Q=\frac{12}{2}=6 \mathrm{~cm}$
Now, $\quad$ area of quadrant $B P Q=\frac{\pi r^{2}}{4}=\frac{3.14 \times(6)^{2}}{4}=\frac{113.04}{4} \mathrm{~cm}^{2}$
Area of four quadrants $=\frac{4 \times 113.04}{4}=1123.04 \mathrm{~cm}^{2}$
Now, $\quad$ area of square $A B C D=(12)^{2}=144 \mathrm{~cm}^{2}$
$\therefore$ Area of the shaded region $=$ Area of square $-$ Area of four quadrants
$=144-113.04=30.96 \mathrm{~cm}^{2}$