ABCD is a square. A circle is inscribed in the square. Also taking A, B, C, D as the centres, four quadrants are drawn inside the

Question

ABCD is a square. A circle is inscribed in the square. Also taking A, B, C, D as the centers, four quadrants are drawn inside the circle touching each other at the mid-points of the sides of the square. Area of the square is 4 cm². What is the area of the shaded region?

(a) \(\big(4 - \frac{3\pi}{2}\big)\) cm² 

(b) (2π – 4) cm² 

(c) (4 – 2π) cm² 

(d) \(\big(4 - \frac{\pi}{2}\big)\) cm²

Answer 1

Answer : (b) (2π – 4) cm² 

From the three figures, we can see that, 

Area of shaded region = Area of the square – (Total area shown by region a + Total area shown by region b) 

The total area of the region a = Area of the square – area of the inscribed circle

Total area of region b = Area of square – 4(Area of a quadrant)

= 4 - 4\(\big(\frac{1}{4} \pi \times (1)^2\big) \) = (4 - π)

∴ Required area = 4 – (4 – π + 4 – π) 

= (2π – 4) cm².