Question 1118750
hexagon and apothem....

Hexagon:  Regular polygon with six congruent sides.
Apothem: Segment whose endpoints are center of a regular polygon and midpoint of one of the sides.


Draw the description!  Can you identify one or two special right triangles which will help you from there?


I do not show a picture here but only describe one this much:
Hexagon is composed of six congruent equilateral triangles.  If apothem a is the height, and one side is 2x, then the apothem cuts equilateral triangle into two special 30-60-90 right triangles, each also with leg x.


Your apothem, a is given but x can be solved for...
{{{(2x)^2=a^2+x^2}}}

Can you continue from here?


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1 equilateral triangle area,  {{{(1/2)(2x)*a=a*x}}}.

6 of these to make the hexagon area,  {{{6*a*x}}}.