In the given figure, ABCD is a square each of whose sides measures 28 cm. Find the area of the shaded region. [Take π = 22/7]
Length of the sides of square = 28 cm
Area of square = a2 = 282 cm2
= 784 cm2
Since, all the circles are identical so, they have same radius
Let the radius of circle be R cm
From the figure 2R = 28 cm
R = 28/2 cm
R = 14 cm
Quadrant of a circle subtends 90° at the centre.
Area of quadrant of circle =
= 22/7 × 14 × 14 × 90°/360° cm2 = 154 cm2
Area of 4 quadrants of circle = 154 × 4 cm2 = 616 cm2
Area of shaded region = Area of square – Area of 4 quadrants of circle
= 784 cm2 – 616 cm2
= 168 cm2