Problem: A regular dodecagon (12 sides) is inscribed in a circle with radius r inches. The area of the dodecagon, in square inches, is:
Answer Choices:
A. 3r2
B. 2r2
C. 3r23/4
D. r23
E. 3r23
Solution:
The dodecagon can be decomposed into 12 congruent triangles like triangle OAB shown. ( AB is a side of the polygon).
area(△OAB)=21rh=21r⋅2r=4r2
∴ area (dodecagon) =12⋅4r2=3r2
