A regular polygon is a polygon with equal sides and angles. Since our dodecagon is regular, the radius of the circumscribed circle of a regular polygon is found by the formula: R = a / 2 * sin (360/2 * n)), where n is the number of corners of the polygon. In our case, n is 12, so sin (360/2 * n) = sin (360/2 * 12) = sin (360/24) = sin 90. Recall that the sine of 90 degrees is 1. Substituting the values into the formula , we can find the value of the side of the dodecagon: 10 = a / 2 * 1, 10 = a / 2, a = 2 * 10 = 20.
Answer: side is 20.
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