Question

In the following figure, a rectangle ABCD enclosed three circles. If BC = 14 cm, find the area of the shaded portion (Take π = 22/7)

Answer 1

To calculate the area of the shaded portion, we need to subtract the total area of the three circles from the area of the rectangle.

• Length of BC (Rectangle's width): 14 cm
• The three circles are identical, and their diameters fit perfectly along the length of the rectangle (AD).

Thus: Diameter of each circle = `("Length of AD (Rectangle)")/("Number of circles")"`

`= 14/3 = 14/3 cm`

Radius of each circle = `"Diameter"/2 = 14/6 = 7/3 cm`

Step 1: Area of the rectangle

Area of Rectangle = Length × Width = AD × BC.

AD = 14 cm, BC = 14 cm.

Area of Rectangle = 14 × 14 = 96 cm²

Step 2: Total area of the three circles

Area of one circle = πr².

`r = 7/3 cm, pi=22/7`

Area of one circle `= 22/7xx(7/3)^2=22/7xx49/9=1078/63 cm^2`

Total Area of Circles `= 3xx1078/63 = 3234/63 = 51.33 cm^2`

Step 3: Area of the shaded portion

Shaded Area = Area of Rectangle − Total Area of Circles.

Shaded Area = 196 − 51.33 = 144.67 cm².

The area of the shaded portion is approximately: 144.67 cm²