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.

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

A = 1/2absin(theta)

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

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

for the entire polygon i did 12(1/2sqrt(2)) = 3sqrt(2)

but then the answer says it's 3

what am i doing wrong?