Question

In the given figure, ABCD is a square of side 4 cm. A quadrant of a circle of radius 1 cm is drawn at each vertex of the square and a circle of diameter 2 cm is also drawn. Find the area of the shaded region. [Use π = 3.14.]

Answer 1

Side of square = 4 cm

Radius of circle = 1 cm

Area of square = (side)² = 4 x 4 = 16 cm²

Area of four quadrants of circle = 4 (1/4 x 3.14 x 1 x 1) = 3.14 cm²

Area of circle with diameter 2 cm = πr² = 3.14 x 1 x 1 = 3.14 cm²

(diameter = radius/2)

Now,

Area of the shaded region = Area of square – (Area of four quadrants of circle + Area of circle with diameter 2 cm)

= 16 – (3.14 + 3.14)

= 9.72

Therefore, the Area of the shaded region is 9.72 cm².