MathDB

Vertex

E

of equilateral

\triangle{ABE}

is in the interior of unit square

ABCD

. Let

R

be the region consisting of all points inside

ABCD

and outside

\triangle{ABE}

whose distance from

\overline{AD}

is between

\frac{1}{3}

and

\frac{2}{3}

. What is the area of

R

? (A)\ \frac{12\minus{}5\sqrt3}{72} \qquad (B)\ \frac{12\minus{}5\sqrt3}{36} \qquad (C)\ \frac{\sqrt3}{18} \qquad (D)\ \frac{3\minus{}\sqrt3}{9} \qquad (E)\ \frac{\sqrt3}{12}

Problem Statement