Question

In Figure 4, 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

ABCD is a square. A quadrant of circle of radius 1 cm is drawn at each vertex of the square.

The quadrant of a circle is a sector of angle 90°.

`\text{Area of each quadrant) =` `pi90^@/360^@=(r^2)3=1_1^4,4xx(1cm)  0.785 cm`

Area of square = (Side)² = (4 cm)² = 16 cm²

Diameter of the circle = 2 cm

∴ Radius of the circle = 1 cm

∴ Area of circle = πr² = 3.14 × (1 cm)² = 3.14 cm²

Area of shaded region

= Area of square − Area of circle − (4 × Area of each quadrant)

= 16 cm² − 3.14 cm² − (4 × 0.785 cm²)

= 16 cm² − 3.14 cm² − 3.14 cm²

= 16 cm² − 6.28 cm²

= 9.72 cm²

Thus, the area of the shaded region is 9.72 cm².