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When Two Congruent Equilateral Triangles Share A Common Center, Their Union Can Be A Star, As Shown. If Their Overlap Is A Regular Hexagon With An Area Of 60, What Is The Area Od One Of The Original Equilateral Triangles?

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Given, the area of the hexagon formed by the overlap of two equilateral triangles is 60.
Let the side of that hexagon is a,
thn area of hexagon is:3 * sqrt(3) * a * a=60   - - - eq(1)
and the side of the triangle : 3a (since side of hexagon is assumed as a)
Therefore area of original equilateral triangle is: (srqt(3)  * (3a) *(3a) ) / 2
  by rearranging the above terms  ((3 * sqrt(3) * a * a) * 3 )/2
  substituting eq(1) we get (60 * 3)/2
  =90.
Therefore area of original equilateral triangle is: 90.

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