Perimeter of a regular hexagon inscribed in a circle = 48 m Find the side of a square inscribed in the same circle.
| June 30, 2021 | education
Since the hexagon is regular, the lengths of all its faces are equal. Then AB = P / 6 = 48/6 = 8 cm.
In a regular hexagon, its edge is equal to the radius of the circumscribed circle, then AO = AB = R = 8 cm.
The diagonal KH of the square KMHP inscribed in a circle is equal to the diameter of the circumscribed circle, then KH = 2 * R = 2 * 8 = 16 cm.
The diagonal KH of the square divides it into two right-angled isosceles triangles, then:
2 * KP ^ 2 = KH ^ 2.
КP ^ 2 = 16/2 = 8.
КP = 2 * √2 cm.
Answer: The length of the side of the square is 2 * √2 cm.
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