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Circle: Area of a Segment

ACTMAT-JELIIN

An equilateral triangle with side length s is inscribed in a circle, dividing the interior of the circle into a triangle and three “segments” of the circle (refer to the figure below).

What is the area of each segment of the circle, in terms of s?

A

$ {\cfrac { { s }^{ 2 } }{ 12 } (2\pi -\sqrt { 3 } )} $

B

$ \cfrac { { s }^{ 2 } }{ 12 } (2\pi -3\sqrt { 2 } ) $

C

$ \cfrac { { s }^{ 2 } }{ 12 } (2\pi -3\sqrt { 3 } ) $

D

$ \cfrac { { s }^{ 2 } }{ 12 } (3\pi -2) $

E

$ \cfrac { { s }^{ 2 } }{ 12 } (4\pi -3\sqrt { 3 } ) $