A regular octahedron has side length 1. A plane parallel to two of its opposite faces cuts the octahedron into two congruent solids. The polygon formed by the intersection of the plane and the octahedron has area \dfrac{a \sqrt{b}}{c}, where a, b, and c are positive integers, a and c are relatively prime, and b is not divisible by the square of any prime. What is a+b+c ?
Answer Choices
A. 10
B. 11
C. 12
D. 13
E. 14