A regular 6 square is inscribed in a circle, the perimeter is 216 cm, find the length of the radius of the circle

Since a regular hexagon is inscribed in a circle, the degree measure of the arc formed by one face of the hexagon will be equal to: arc AB = 360/6 = 60.

Then the central angle of AOB is also equal to 60.

The AOB triangle is equilateral, since OA = OB = R, and since one of the angles of the triangle is 60, this triangle is equilateral, which means AB = R. Since the hexagon is regular, then all of its faces are equal to the radius of the circumscribed circle, which and it was required to prove.