# The side of a regular hexagon is 8. Find the smaller diagonal of the hexagon

August 29, 2021 | education

| Determine the size of the inner corner of a regular hexagon.

Angle ABC = (n – 2) * 180 / n, where n is the number of sides of the polygon.

Angle ABC = (6 – 2) * 180/6 = 720/6 = 1200.

In the triangle ABC, by the cosine theorem, we define the length of the AC side.

AC ^ 2 = AB ^ 2 + BC ^ 2 – 2 * AB * BC * Cos120 = 64 + 64 – 2 * 8 * 8 * (-1/2) = 128 + 64 = 192.

AC = 8 * √3 cm.

Answer: The length of the smaller diagonal is 8 * √3 cm.

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