Question

In the figure, ABCD is a square whose sides are of length 2 cm. The midpoints of sides AB, BC, CD and DA are respectively P, Q, R and S. Four arcs are drawn with A, B, C and D as centres and AP as radius. Area of shaded portion is

• A. $(4-\frac{\pi }{3})sq.cm$
• B. $(4-\pi )sq.cm$
• C. $(2-\frac{\pi }{2})sq.cm$
• D. $(3-\frac{\pi }{7})sq.cm$

Answer 1

The correct option is B $(4-\pi )sq.cm$

Given, side of square ABCD $=2cm$

Area of square ABCD = $2\times 2=4sq.cm$
Area of APS $=\frac{1}{4}\pi r^2$
$\Rightarrow \frac{1}{4}\pi (1{)}^2=\frac{\pi }{4}$

$\because$ Area of APS $=$ Area of BPQ$=$Area of CQR=Area of DRS
$\therefore$ Area of non shaded region$=$ $4\times \frac{\pi }{4}=\pi$

Area of shaded region$=$Area of square ABCD-Area of non-shaded region
$\Rightarrow (4-\pi )sq.cm.$
Hence,option B is correct.