AHSME 1995 Problem 19

Equilateral triangle $DEF$ is inscribed in equilateral triangle $ABC$ such that $\overline{DE} \perp \overline{BC}$. The ratio of the area of $\triangle DEF$ to the area of $\triangle ABC$ is $\mathrm{(A) \ \frac {1}{6} } \mathrm{(B) \ \frac {1}{4} } \mathrm{(C) \ \frac {1}{3} } \mathrm{(D) \ \frac {2}{5} } \mathrm{(E) \ \frac {1}{2} }$