area of a regular hexagon

Question

hi

can some one share the formula for finding the area of a regular hexagon just by using :

1 only the side

2 only Altitude from center to one of the sides

thanks

Bunuel · Answer

Area of a regular polygon: https://www.mathopenref.com/polygonregulararea.html

Rogalik · Answer

I will think so:

1) regular hexagon consists of 6 equilateral triangles. So using the area formula for eauilateral triangle:
S = 6 * (a^2 * 3^(1/2) /4) = 3*3^(1/2)*a^2

2) similar, find the side of eauilateral triangle though it's height and put inside previous formula. 
a= 2/(3^(1/2)) * h

144144 · Answer

thanks for the link.

gmatpapa · Answer

A regular hexagon can be divided into 6 equilateral triangles of equal area, with all sides of respective triangles (except of course, the side that is a part of the hexagon), meeting at the center of hexagon. 1. If one side is known, you can calculate the area of one equilateral triangle by calculating its altitude first (the altitude of an equilateral triangle= (sqrt3) / 4) then calculating its area ( \frac{1}{2}* base* altitude ). Multiply this area by 6 (as there are 6 similar triangles of equal area) and you have the area for the hexagon. 2. Divide hexagon into 6 equilateral triangles. The altitude from the center to the side is equal to the altitude of each one of the equilateral triangle. If you know the altitude of an equilateral triangle, you can calculate its sides. So, the area of 1 equilateral will be \frac{1}{2}*altitude*base . multiply the value by 6 and you're good

area of a regular hexagon

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