The area of a circle inscribed in a regular hexagon is 60.75 pi sq. find the perimeter of the hexagon.

The radius of a circle inscribed in a regular hexagon is determined by the formula:

r = a * √3 / 2, where a is the side of the hexagon.

Area of a circle inscribed in a regular hexagon:

S = n * r ^ 2 = n * a ^ 2 * 3/4.

By condition, the area of this circle is 60.75p, therefore:

n * a ^ 2 * 3/4 = 60.75 * n;

a ^ 2 = 60.75 * 4/3 = 81;

a = √81 = 9 is the side of this hexagon.

The desired perimeter of a regular hexagon:

P = 6 * a = 6 * 9 = 54.