AMC 10A 2010 Problem 19

Equiangular hexagon A B C D E F has side lengths A B=C D=E F=1 and B C=D E=F A=r. The area of \triangle A C E is 70 \% of the area of the hexagon. What is the sum of all possible values of r ?

Answer Choices
A. \dfrac{4 \sqrt{3}}{3}
B. \dfrac{10}{3}
C. 4
D. \dfrac{17}{4}
E. 6