A dodecagon is a polygon with twelve sides and twelve angles. Dodecagon may be a convex or a concave polygon.Dodecagon Picture
The above figure is a dodecagon with twelve vertices named from A through L. In the above dodecagon, the sides are of varying length. It is to be noted that the sides need not be of the same length.

A Regular Dodecagon is a dodecagon in which all twelve sides are of equal lengths. As all the sides are of equal length, all the angles will be equal.
Each interior angle is equal to 150o. Sum of interior angles = 1800o.

Regular Dodecagon
The above polygon is a regular decagon with each side is of 2 unit length.

We can construct a dodecagon by following the steps given hereunder:
Step 1: Draw a straight line and take a point O on it. Draw a circle with center O. Let A and B be the points where the line intersects the circle. Then, AB is the diameter and hence OA=OB=r, the radius of the circle.

Solving Regular Dodecagon

Step 2: Draw an arc of radius equal to the diameter 2r with centers at A and B. Let the intersecting points of the arcs be X and Y.

How to Solve Regular Dodecagon

Step 3: Join X and Y with a straight edge. The line segment $\overline{XY}$ will be perpendicular to the line segment $\overline{AB}$. Suppose that the line segment $\overline{XY}$ intersects the circle at the points C and D.
Steps to Solve Regular Dodecagon

Step 4: Draw arcs with radius equal to r with centers A, B, C, and D. Let the intersecting points of the arcs with the circle be V1, V2, V3, V4, V5, V6, V7 and V8. Join each point (including A, B, C, D) with its adjacent point using a straight edge.
Step to Solve Regular Dodecagon

By removing the arcs and circumscribed circle, we get a dodecagon.
Solve Regular Dodecagon Problems