...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: .
A = pi/4 / 2 = (1/sqrt(2))/2 = 1/2sqrt(2) - for 1 triangle
for the entire triangle i did 12(1/2sqrt(2)) = 3sqrt(2) <--- the value in red is wrong. See above!
but then the answer says it's 3
what am i doing wrong?