Question 1118750
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The area of a regular hexagon is six times the area of central equilateral triangle.


You are given the apothem = {{{2*sqrt(3)}}} of the regular hexagon, which is the altitude of the equilateral triangle.


Let x be the side length of the hexagon.

It is also the side length of the equilateral triangle.


In an equilateral triangle with the side length x the altitude is  {{{x*(sqrt(3)/2))}}}.   //  Every student who study/studied Geometry must know it.


Therefore,  {{{x*(sqrt(3)/2)}}} = {{{2*sqrt(3)}}},  which implies  x= 4.


Thus the side length of the regular hexagon is 4 units, same as the side length of the equilateral triangle.


Hence, the area of the equilateral triangle is  {{{(1/2)*4*(4*sqrt(3)/2)}}} = {{{4*sqrt(3)}}} square units.


Then the area of the given hexagon is 6 times this value, i.e. {{{24*sqrt(3)}}} square units.
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