MathDB

In the star shaped figure below, if all side lengths are equal to

3

and the three largest angles of the figure are

210

degrees, its area can be expressed as

\frac{a \sqrt{b}}{c}

, where

a, b

, and

c

are positive integers such that

a

and

c

are relatively prime and that

b

is square-free. Compute

a + b + c

. https://cdn.artofproblemsolving.com/attachments/a/f/d16a78317b0298d6894c6bd62fbcd1a5894306.png

Problem Statement