In the given figure, an equilateral triangle has been inscribed in a circle of radius 4 cm. Find the area of the shaded region. [Take π = 3.14 and √3 = 1.73]
Radius of circle = R = 4 cm
OD perpendicular to AB is drawn
ΔABC is equilateral triangle,
∠A = ∠B = ∠C = 60°
∠OAD = 30°
OD/AO = sin 30°
AO = 4 cm
OD = 1/2 × 4 cm
OD = 2 cm
AD2 = OA2 – OD2
= 42 – 22 = 16 – 4 = 12 cm2
AD = 2√3 cm
AB = 2 × AD
= 2 × 2√3 cm = 4√3 cm
Area of triangle ABC = √3/4 × AB2
= √3/4 × 4√3 × 4√3
= 20.71 cm2
Area of circle = πR2
= 3.14 × 4 × 4 cm2
= 50.24 cm2
Area of shaded region = 29.53 cm2
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