Problem
1996 AHSME Problem 19
The midpoints of the sides of a regular hexagon ABCDEF are joined to form a smaller hexagon. What fraction of the area of ABCDEF is enclosed by the smaller hexagon?
![[asy] size(120); draw(rotate(30)*polygon(6)); draw(scale(2/sqrt(3))*polygon(6)); pair A=2/sqrt(3)*dir(120), B=2/sqrt(3)*dir(180), C=2/sqrt(3)*dir(240), D=2/sqrt(3)*dir(300), E=2/sqrt(3)*dir(0), F=2/sqrt(3)*dir(60); dot(A^^B^^C^^D^^E^^F); label("$A$", A, dir(origin--A)); label("$B$", B, dir(origin--B)); label("$C$", C, dir(origin--C)); label("$D$", D, dir(origin--D)); label("$E$", E, dir(origin--E)); label("$F$", F, dir(origin--F)); [/asy]](/static/aops/66664d57ff464bea26c246e5fa7e1f2fa9f9bbea.png)
\text{(A)}\ \frac{1}{2}\qquad\text{(B)}\ \frac{\sqrt 3}{3}\qquad\text{(C)}\ \frac{2}{3}\qquad\text{(D)}\ \frac{3}{4}\qquad\text{(E)}\ \frac{\sqrt 3}{2}
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