Let A B C D E F be an equiangular hexagon. The lines A B, C D, and E F determine a triangle with area 192 \sqrt{3}, and the lines B C, D E, and F A determine a triangle with area 324 \sqrt{3}. The perimeter of hexagon A B C D E F can be expressed as m+n \sqrt{p}, where m, n, and p are positive integers and p is not divisible by the square of any prime. What is m+n+p ?
Answer Choices
A. 47
B. 52
C. 55
D. 58
E. 63