# Find the side of a regular hexagon inscribed in a circle with a radius of 5 m.

August 27, 2021 | education

| The area of a regular nentagon is equal to ten areas of isosceles triangles AOB, formed by the radii of a circle drawn to the vertices of the nentagon.

Determine the value of the central angle AOB.

Angle AOB = 360/10 = 36.

In an isosceles triangle AOB, OA = OB = R = 5 m, angle AOB = 36, then by the cosine theorem we determine the length of the side AB.

AB ^ 2 = ОА ^ 2 + ОВ ^ 2 – 2 * ОА * ОВ * Cos36 = 25 + 25 – 2 * 5 * 5 * 0.81 = 50 – 40.5 = 9.5.

AB = 3.08 m.

Answer: The length of the side of the decagon is 3.08 m.

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