# Find the radius of a circle around a regular hexagon if its smaller diagonal is 12.

July 26, 2021 | education

| Data: dm is the smaller diagonal of the considered regular hexagon (dm = 12 units).

To find out the required radius of the circle, we will use the formula: R = a / (2 * sin 30) = a (side of the hexagon) = dm / √3.

Let’s calculate: R = dm / √3 = 12 / √3 units ≈ 6.93 units.

Answer: The radius of the circle, according to the calculation, should be 12 / √3 units (6.93 units).

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