MathDB

A regular hexagon with center at the origin in the complex plane has opposite pairs of sides one unit apart. One pair of sides is parallel to the imaginary axis. Let

R

be the region outside the hexagon, and let S\equal{}\{\frac{1}{z}|z\in R\}. Then the area of

S

has the form a\pi\plus{}\sqrt{b}, where

a

and

b

are positive integers. Find a\plus{}b.

Problem Statement