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a regular hexagon is composed of 12 congruent 30,60,90 degree triangles. if the length of the hypotenuse of one of those triangles is 18 square root 3 find the perimeter of the hexagon

  • geometry -

    let x be the base of one of those triangles.
    cos 60° = x/(18√3)
    x = 18√3 cos 60°
    = 18√3(√3/2) = 9
    but x would be 1/2 of one of the sides of the hexagon
    so each side is 18
    and the perimeter = 6(18) or 108

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