Picture is attached. I want to use similarity to find the ratio but am not sure where to start. Hints are appreciated.
2026-04-03 18:47:26.1775242046
Ratio of shaded area to that of one of the 5 congruent triangles
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Let $a$ denote side length of an equilateral triangle. Then, the area of one equilateral triangle is $A=\frac12 (a)(a)\sin60^\circ$.
By similarity of triangles, we can find marked lengths in the figure below.
Therefore the area of shaded triangle on left is $\frac12(a)(\frac45a)\sin 60^\circ=\frac45A$
Using the property, "similar triangles are to one another in the squared ratio of (their) corresponding sides" [1], we can find other shaded areas as well.
Can you take it from here?