A regular hexagon with a side of 4 cm is inscribed in the circle. Find the side of the square described around this circle.

univerkov | March 4, 2021 | education

We have a regular hexagon, with sides equal to 4 cm. The circle is described about a hexagon, by the property of a circle described around a regular hexagon, its radius is equal to the side of the hexagon r = a = 4 cm.
Around the circle, a square is described, by the property of a circle inscribed in a square, its radius is equal to half of the side of the square:
r = s / 2
Hence:
c = 2 * r = 2 * 4 = 8 cm.
Answer: the side of the square is 8 cm.

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