hexagon: area of reg. hexagon w/ sides 12 inches long

[tamiatha]

what is the area of a regular hexagon whose sides are each 12 inches long. round to nearest square inch.
my solution:
A = 4 (1) + 4 (0.5)
A=6
i did not use the info about the side length therefore my answer is wrong

 

[Loren]

Draw a regular hexagon. From the center of the hexagon draw a line to each of two consecutive vertices. You now have what kind of triangle? Draw the apothem of the hexagon which is the altitude of the triangle. Now, you should see that you have at least one right triangle. You can figure out the length of the short leg of the triangle and the length of the hypotenuse of the triangle. Use the Pythagorean theorem to find the altitude of the triangle. Now, find the area of the triangle. Now, figure out what to multiply that by to get the area of the hexagon.

 

[tamiatha]

i drew the hexagon
i have equilateral triamgles
i am lost from there
you gave good info
i just do not understand how to get the info i need

 

[Loren]

In one of the triangles, draw an altitude. Does this create two right triangles? How long is the hypotenuse? How long is the short leg? Using the Pythagorean Theorem, how long is the long leg. Now, can you determine the area of the triangle?

 

[pka]

Take a close look at this webpage: http://mathworld.wolfram.com/Hexagon.html.
Look at formular (4).