Level pending

Dan wants to create the Adidas logo by cutting three strips of same sized rectangles with the width 6, labelled $$ABCD, EFGH, KLMN$$ respectively. Then, he cuts the strips diagonally, at $$QR$$, such that $$\cos\angle BQR=0.5$$. This process continues at the other two rectangles, at $$ST$$ and $$UV$$ respectively, by satisfying $$\cos\angle FST = \cos\angle LUV=0.5$$. If the ratio of the area of the trapeziums is $$[ABQR]:[EFST]:[KLUV]=65:34:13$$, and the sum of the areas is 336, then find $$\lfloor BQ+FS+LU\rfloor$$ if $$BQ>AR, FS>ET, LU>KV$$.

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