Originally Posted by

**dondonlouie** I'm having a hard time solving this problem:

Find the area of a regular dodecagon whos vertices are 12 equally spaced points on the unit circle. **<--- OK**

what i did was split the entire polygon into 12 smaller triangles

A = 1/2absin(theta)

A = 1/2 (1)(1)sin(pi/4)

**The central angle of one triangle is calculated by: $\displaystyle \frac{2 \pi}{12}=\frac16 \pi$.**

**... and $\displaystyle \sin\left(\frac16 \pi\right)=\frac12$**

A = pi/4 / 2 = (1/sqrt(2))/2 = 1/2sqrt(2) - for 1 triangle

for the entire triangle i did 12(1/2**sqrt(2)**) = 3sqrt(2) **<--- the value in red is wrong. See above!**

but then the answer says it's 3

what am i doing wrong?