# The perimeter of a square inscribed in a circle is 24 cm. Find the side of a regular hexagon inscribed in the same circle.

If the perimeter of a square is 24 cm, then its side is 24/4 = 6 cm.

The diameter of a circle circumscribed about a square is equal to the diagonal of this square. By the Pythagorean theorem, the square of the diagonal is equal to the sum of the squares of the two sides:

D ^ 2 = a ^ 2 + a ^ 2 = 6 ^ 2 + 6 ^ 2 = 2 * 36;

D = 6√2 cm.

The radius is equal to half the diameter, which means that the radius of the circumscribed circle around this square is 3√2 cm.

It is known that the side of a regular hexagon is equal to the radius of the circumscribed circle. This means that the required side of a regular hexagon is 3√2 cm.

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