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

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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?

posted Jan 21, 2016

–1 vote

Let's side of equilateral triangle=a
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
ans is 1.843

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

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

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 May 18, 2020 by anonymous
–1 vote

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

same comment as above.

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