Question

Find the area of an equilateral triangle (regular 3-gon) with the given measurement.
6-inch apothem
A = sq. in.

Please explain your answer

Answer 1

what exactly is the apothem?

Answer 2

the perpendicular distance from the center of the polygon to a side.

Answer 3

Isn't this just the same question as last time?

Answer 4

No it has "apothem" now

Answer 5

OK, not exactly...

Answer 6

You can just use cos or sin to turn it into the same type of problem...

Answer 7

okay fine
then the apothem will also be a part of the median
& in properties of triangle it divides in the ratio 2:1
hence height is 18inches
the side or side=18*tan30
hecce area=18*18*tan30* 1/2
=162*(1/3)^1/2

Answer 8

sorry i typed side or side
it is side or base

Answer 9

You see what I am saying, you have Sin 30 = apoth/circumradius.

Once you have circumradius use the same formula as last time.

Answer 10

How would I find the circumradius?

Answer 11

Like I said, you have Sin 30 = apoth/circumradius so

circumradius = apoth/Sin 30 = 6/0.5 = 12.

Answer 12

Oh okay, thanks!

Sorry, imma little bit slow today

Answer 13

np, just makes your life a bit easier if u can reuse something u already know.

Answer 14

Truth is, all this geometry stuff confuses me.

Answer 15

A lot of stuff is here http://en.wikipedia.org/wiki/Triangle

Comes up all the time, one way or another.

Answer 16

Thanks you :)

Answer 17

hi kraken the area A=3(SQRT3)a^2
A=3(SQRT3)(6)^2=187.06 ans