Four regular hexagons surround a square with a side length 1, each one sharing an edge with the square, as shown in the figure below. The area of the resulting 12-sided outer nonconvex polygon can be written as m \sqrt{n}+p, where m, n, and p are integers and n is not divisible by the square of any prime. What is m+n+p ?
Answer Choices
A. -12
B. -4
C. 4
D. 24
E. 32