Question 32
$AB$ and $CD$ are two segments, both long $4$, having the midpoint $M$ in common and such that $B \widehat{M} D = 60^\circ$. We indicate by $X$ the set of all and only the points that are at most $1$ distant from at least one of the two segments. What is the surface area of $X$?
(A) $8 - \frac{4}{3} \sqrt{3}$
(B) $16 - \frac{8}{3} \sqrt{3}$
(C) $16 - \frac{4}{3} \sqrt{3} + \pi$
(D) $16 - \frac{8}{3} \sqrt{3} + 2\pi$
(E) $8 + 2\pi$.
(A) $8 - \frac{4}{3} \sqrt{3}$
(B) $16 - \frac{8}{3} \sqrt{3}$
(C) $16 - \frac{4}{3} \sqrt{3} + \pi$
(D) $16 - \frac{8}{3} \sqrt{3} + 2\pi$
(E) $8 + 2\pi$.