Question

find the area of the shaded region in the following figure where PQRS is a rectangle 30 cm long and two circles have the same radii (π =3.14)​

Answer 1

Step-by-step explanation:

area of shaded region = area of rectangle-2×area of circle

Answer 2

The area of the shaded region is 355.8 cm².

• The sum of the diameters of both the circles having same radii in the figure is equal to the length of the rectangle. ∵ The line joining the diameters of the circle is parallel to the length and is of equal length.
• Let the radius of the circle be x.

4 × radius of circle = length of the rectangle

4x = 30

x = 7.5 cm

• Now breadth of the rectangle is equal to diameter of the rectangle.

Breadth of rectangle = 2×7.5 = 15 cm.

Length of the rectangle is 30 cm.

• Area of the rectangle = 15 × 30 = 450 cm².

• Area of the circle = 2πr.

Radius of the circle = 7.5 cm

Area of circle = 2×3.14×7.5 = 47.1 cm²

• Area of both the circles = 2×area of circle = 2× 47.1 = 94.2 cm².

• Now,

Area of the shaded portion = Area of rectangle - Area of both the circles

Area of the shaded portion = 450 - 94.2 = 355.8 cm².

• Area of the shaded portion is equal to 355.8 cm².