HMMT 2019 G10

In triangle $A B C, A B=13, B C=14, C A=15$. Squares $A B B_{1} A_{2}, B C C_{1} B_{2}, C A A_{1} C_{2}$ are constructed outside the triangle. Squares $A_{1} A_{2} A_{3} A_{4}, B_{1} B_{2} B_{3} B_{4}, C_{1} C_{2} C_{3} C_{4}$ are constructed outside the hexagon $A_{1} A_{2} B_{1} B_{2} C_{1} C_{2}$. Squares $A_{3} B_{4} B_{5} A_{6}, B_{3} C_{4} C_{5} B_{6}, C_{3} A_{4} A_{5} C_{6}$ are constructed outside the hexagon $A_{4} A_{3} B_{4} B_{3} C_{4} C_{3}$. Find the area of the hexagon $A_{5} A_{6} B_{5} B_{6} C_{5} C_{6}$.