In Fig., a square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm, find the area of the shaded region. (Use π = 3.14)

Given that, Square OABC is inscribed in a quadrant OPBQ. If OA = 20 cm

We know that,  formula for the area of the sector of a circle

Area of the sector = $\frac{\theta }{{360}^0}$ $\times$ ${\mathrm{\pi r}}^2$

In the above figure join OB. After joining OB we get  a right angled triangle with the measure of angle OAB = 90⁰

Thus, OA = AB = 20 cm

by using pythagoras theorem 

OB² = OA² + AB²

= (20)² $+$(20)²

=  $\sqrt{400 +400}$

= 20 $\sqrt{2}$ cm

Hence, Radius of the quadrant = r = OB = 20 $\sqrt{2}$ cm

Area of quadrant OPBQ = $\frac{{90}^0}{{360}^0}$ $\times$ ${\mathrm{\pi r}}^2$

=1/4 $\times$ 3.14 $\times$ (20 $\sqrt{2}$)

= 628 cm²

Area of square = (OA)²

= (20)²

= 400 cm²

Area of the shaded region = Area of quadrant OPBQ $-$ Area of square OABC

= 628 $-$ 400 

= 228 cm²