In a circle of radius 1, an equilateral triangle is inscribed in the circle as shown. What is the area of blue region?

Question

In a circle of radius 1, an equilateral triangle is inscribed in the circle as shown. What is the area of the blue region?

Answer 1

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
A=(1.732/4)*(1.732)^2=1.299
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

Comments

But you make a = square root of 3 = (1.732).   why? when in fact is 1.75

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√3=1.732

Answer 2

Blue area = pi - ( 1.5 x .875 ) or 1.82909 sr units

Answer 3

First, The equilateral triangle is divided into three isosceles triangles of two sides L = 1 and and angles 30, 30 and 120.
Second. The triangle isosceles is divided into two rrectangular triangles.
The hight of the triangle isosceles H = Radius of circle x sen 30, then H = 0,5
The base of the triangle isosceles B = 2 x Radius of the circle x cos 30 = 1,732
Then , tthe area of one triangle is 1,732 x 0,5 / 2
The total area of the internal triangle is 1,732 x 0,5 / 2 x 3 = 1,3
The area of the blue shaded zone is 1 x Pi - 1,3

Answer 4

Area of the blue region = Area of the circle - Area of the triangle
Area of the blue region = π - 3*√3/4 = 1,84

Comments

same comment as above.