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).
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37
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
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