You can put this solution on YOUR website! 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...
Can you continue from here?
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1 equilateral triangle area, .
6 of these to make the hexagon area, .
The area of a regular hexagon is six times the area of central equilateral triangle.
You are given the apothem = 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 . // Every student who study/studied Geometry must know it.
Therefore, = , 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 = square units.
Then the area of the given hexagon is 6 times this value, i.e. square units.
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