Puzzle of the Week #251 - Trispace

I have an equilateral triangle, dissected into three trapezoids and a smaller equilateral triangle. The PERIMETERS of the three trapezoids are 52, 66 and 80 respectively. The side length of the overall equilateral triangle (a) is precisely 13 times the side length of the smaller equilateral triangle (b).

What is the value of a?

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