A circle is described around a square with a side of 2√2 cm, which is inscribed in a regular triangle. Find the area of the triangle.

The radius of a circle circumscribed about a square:

R = a / √2; where a is the side of the square; = 2√2: √2 = 2 (cm);

The radius of a circle inscribed in a regular triangle:

R = b / 2√3, where b is the side of the triangle;

Hence b = 2 √3 R = 2 √ * 2 = 4 √3 (cm);

Regular triangle area:

S = √3 / 4 b² = √3 / 4 * (4 √3) = √3 / 4 * 12 = 3 √3 (cm²);