Question

Find the area of the shaded region in the figure, where arcs drawn with centres, A, B , C and D intersect 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. $20c{m}^2$
• B. $44c{m}^2$
• C. $80c{m}^2$
• D. $31c{m}^2$

Answer 1

The correct option is D

$31c{m}^2$

Given: Side of a square ABCD = 12 cm

Q is the mid - point of BC.

$\therefore Radius=BQ=\frac{12}{2}=6cm$

Now, area of quadrant BPQ $=\frac{\pi r^2}{4}=\frac{3.14\times (6{)}^2}{4}=\frac{113.04}{4}c{m}^2$

Area of four quadrants $=\frac{4\times 113.04}{4}=113.04c{m}^2$

Now, area of square ABCD $=(12{)}^2=144c{m}^2$

$\therefore$ Area of the shaded region = Area of square - Area of four quadrants

$=144-113.04=30.96c{m}^2$ = $31c{m}^2$