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In a circle of radius 1, an equilateral triangle is inscribed in the circle as shown. What is the area of the blue region?
Let's side of equilateral triangle=a
ans radius of circle=R=1
Radius of the circumscribed circle is R=a/root of 3
1=a/root of 3
a=root of 3=1.732...................................................................(i)
Area of equilateral triangle=A=(root of 3/4)*a^2
Area of circle=C=(pi/4)*d^2=(3.142/4)*(2)^2=3.142
Area of shaded portion=C-A=3.142-1.299=1.843
ans is 1.843
Blue area = pi - ( 1.5 x .875 ) or 1.82909 sr units
Area of the blue region = Area of the circle - Area of the triangle
Area of the blue region = π - 3*√3/4 = 1,84
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