A circle has a radius of 6 in. The circumscribed equilateral triangle will have an area of:

The length of the side of an equilateral triangle that is circumscribed by a circle with radius r is s = r sqrt (3)

so s = (6) sqrt (3)

then the formula for the area of an equilateral triangle is

A = sqrt (3) (s^2) / 4

substitute the value of s in the equation

A = sqrt (3) ((6) sqrt (3)) ^2 / 4

A = 46.77 sq in