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Question

A regular hexagon and an equilateral triangle have equal areas. What is the ratio of the length of a side of the triangle to the length of a side of the hexagon?

Accepted Answer

A_ = s_t^234 A_hex = 6s_h^234 since a regular hexagon is just six equilateral triangles. Setting the areas equal, we get: s_t^2 = 6s_h^2 (s_ts_h)^2 = 6 s_ts_h = 6, and the answer is 6.