2021 AMC 10A Problem 21

Let ABCDEF be an equiangular hexagon. The lines AB, CD, and EF determine a triangle with area 192\sqrt{3}, and the lines BC, DE, and FA determine a triangle with area 324\sqrt{3}. The perimeter of hexagon ABCDEF 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?

\textbf{(A)} ~47\qquad\textbf{(B)} ~52\qquad\textbf{(C)} ~55\qquad\textbf{(D)} ~58\qquad\textbf{(E)} ~63

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.