Express the area within the circle, but outside the triangle, as a function of the length of a side of the triangle.

First find the radius of the circle.

Consider the vertex at the left corner is on the origin.

Observe the figure,  vertex at the right corner is .

Find the coordinates of remaining vertex of the triangle.

-coordinate of the vertex is .

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Formula for the center of the triangle is .

Center of the triangle is 

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Find the radius of the triangle.

Radius is the distance between center and origin.

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Formula for the area of the circle .

Area of the equilateral tringle is .

The area within the circle, but outside the triangle

Substitute .

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