AHSME 1993 Problem 17

Amy painted a dartboard over a square clock face using the "hour positions" as boundaries.[See figure.] If $t$ is the area of one of the eight triangular regions such as that between 12 o'clock and 1 o'clock, and $q$ is the area of one of the four corner quadrilaterals such as that between 1 o'clock and 2 o'clock, then $\frac{q}{t}=$ $\text{(A) } 2\sqrt{3}-2 \text{(B) } \frac{3}{2} \text{(C) } \frac{\sqrt{5}+1}{2} \text{(D) } \sqrt{3} \text{(E) } 2$