A square and a regular hexagon are described around a circle. Find the perimeter of the square

univerkov | June 10, 2021 | education

A square and a regular hexagon are described around a circle. Find the perimeter of the square if the perimeter of the hexagon is 48 cm.

Determine the side length of a regular hexagon.

AP = P / 6 = 48/6 = 8 cm.

Triangle AOB is equilateral, in which the segment OH is its height and the radius of the inscribed circle.

OH = √3 * AB / 2.

OH = √3 * 8/2 = 4 * √3 cm.

The length of the side of a square circumscribed about a circle is equal to the length of the diameter of the circle.

A1B1 = 2 * OH = 2 * 4 * √3 = 8 * √3 cm.

Then the perimeter of the square is equal to: Ркв = 4 * А1В1 = 4 * 8 * √3 = 32 * √3 cm.

Answer: The perimeter of the square is 32 * √3 cm.

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