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An equilateral triangle and a regular hexagon have equal perimeters. What is the area of the triangle, if the area of the hexagon is 120?
I don't get it

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Kizzy

  1. the triangle can be formed by joining alternate vertices of the hexagon. So, if the hexagon has side s, the triangle has side s√3

    Now the hexagon consists of sic equilateral triangles of side s, so its area is

    6(s^2 √3/4) = 3√3/2 s^2

    The triangle has area

    √3/4 (s√3)^2 = 3√3/4 s^2

    The ratio of areas is thus

    (3√3/4 s^2) / (3√3/2 s^2) = 1/2

    So the triangle has area 60

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    Steve

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