Yay for 2014! #7

Geometry Level 4

Let ABDCABDC be a rectangle, as shown above, such that AB=20AB = 20 and AC=14.AC = 14. Points EE and FF are located in the interior of ABDCABDC such that the triangles AECAEC and BFDBFD are equilateral. The area of the intersection of these triangles can be represented by

a3bc,\frac{a\sqrt{3}}{b}- c,

where a,b,a, b, and cc are positive integers with gcd(a,b)=1.\gcd(a, b) = 1. Find a+b+c.a+b+c.

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