Question

In the following figure, an equilateral triangle ABC of side 6 cm has been inscribed in a circle. Find the area of the shaded region. (Take π = 3.14).​

Answer 1

Answer:

The area of shaded region is 22.1 cm²

Step-by-step explanation:

Given :

Side of an equilateral ∆ABC ,(a )= 6 cm

Radius of circumcircle ,r = side of equilateral triangle/√3

r = 6/√3  

r = 6 × √3/ (√3 ×√3)

r = 6√3/3

r = 2√3 cm

Radius of circumcircle ,r = 2√3 cm

Area of circle ,A1 = πr²

A1 = 3.14 × (2√3)²

A1 = 3.14 × 4 × 3

A1 = 3.14 × 12

A1 = 37.68 cm²

Area of circle ,A1 = 37.68 cm²

Area of equilateral  ∆ABC, A2 = √3/4 × side²

A2 = √3/4 × 6²

A2 = √3/4 × 36

A2 = √3 × 9

A2 = 1.732 × 9

A2 = 15.58

Area of equilateral  ∆ABC =  15.58  cm²

Area of shaded region,A =  Area of circle -  Area of equilateral  ∆ABC

A = A1 - A2

A = 37.68 - 15.58

A = 22.1 cm²

Area of shaded region = 22.1 cm²

Hence, the area of shaded region is 22.1 cm²

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer:

Step-by-step explanation:

Attachment is given below