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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 blue region?

+2 votes
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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?

What is the area of the blue region

posted Jan 21, 2016 by anonymous

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3 Answers

–1 vote
 
Best answer

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

answer Jan 21, 2016 by Jaikumar Bhatia
But you make a = square root of 3 = (1.732).   why? when in fact is 1.75
0 votes

enter image description here

Blue area = pi - ( 1.5 x .875 ) or 1.82909 sr units enter image description here

answer Apr 30 by Juan Carlos Saavedra
–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

answer Oct 8, 2017 by Halil Akansel
same comment as above.



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