The side of a regular quadrilateral circumscribed about a certain circle is 8

The side of a regular quadrilateral circumscribed about a certain circle is 8. Find the area of a regular triangle circumscribed about the same circle.

Given: a regular quadrilateral ABCD is described around a circle;
a = AB = BC = CD = DA = 8 cm;
Find S MHK -? (Where the regular triangle MHK is described around the same circle)
Decision:
1) the radius of the inscribed circle is found by the formula r = a / 2 = 8/2 = 4 cm;
2) find the side of a regular triangle circumscribed about this circle, that is, MH = HK = MK = 2√3 * r = 2√3 * 4 = 8√3 (cm);
3) S MHK is found by the formula S = r * p, p = 8√3 * 3/2 = 4 * 3√3 = 12 √3, then S MHK = 4 * 12 √3 = 48√3 (cm ^ 2 ).
Answer: 48√3 cm ^ 2