# Find the area of a regular dodecagon if the radius of the circumscribed circle is 10

October 17, 2021 | education

| 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.

One of the components of a person's success in our time is receiving modern high-quality education, mastering the knowledge, skills and abilities necessary for life in society. A person today needs to study almost all his life, mastering everything new and new, acquiring the necessary professional qualities.