SOLUTION: I need to find the side length of a 6 sided polygon with an apothem of 14 in. so that I may find the area. Please help me in simple language on HOW TO FIND A SIDE LENGTH to use in

Question 566763: I need to find the side length of a 6 sided polygon with an apothem of 14 in. so that I may find the area.
Please help me in simple language on HOW TO FIND A SIDE LENGTH to use in formula A=1/2aP.
Thank you so much!
Answer by scott8148(6628) (Show Source): You can put this solution on YOUR website!
a 6 sided polygon (hexagon) consists of 6 equilateral triangles joined at a common vertex (the center of the hexagon)

the side length you want is the side of an equilateral triangle that has an altitude of 14

the altitude of an equilateral triangle bisects the base and forms two congruent 30-60-90 right triangles

the ratio of the sides of a 30-60-90 triangle is ___ 1 : 2 : sqrt(3)

in this case, the ratio represents ___ (s / 2) : s : 14

so ___ 14 / [sqrt(3)] = s / 2

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