SOLUTION: Hi...this would be extremely beneficial for me if somebody could help with this problem: Find the length of each side of a regular hexagon if opposite sides from midpoint to midpo

Question 80365: Hi...this would be extremely beneficial for me if somebody could help with this problem: Find the length of each side of a regular hexagon if opposite sides from midpoint to midpoint are 18 inches apart.

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
Find the length of each side of a regular hexagon if opposite sides from midpoint to midpoint are 18 inches apart.
--------
Draw the picture.
Notice that half of the line segment connecting the opposite midpoints
is the perpendicular bisector of a triangle formed by connecting
the center to the two adjoining vertices.
That perpendicular bisector is 9 inches long
The base angles of that triangle are each 60 degrees because the figure
is a regular hexagon. The smaller angle in the little triangle formed
s 30 degrees. So the side opposite is half the hypotenuse.
Let the hypotenuse be 2x; then the smaller side is x.
Use Pythagoras to get:
(2x)^2= x^2 + 9^2
3x^2=81
x^2=27
x=3sqrt3
That is hal the lenth of the side.
So the side is 6sqrt3
==========
cheers,
stan H.
RELATED QUESTIONS
Hello, im wondering if you can help me figure out the formula to find: If 6750 red... (answered by Boreal,alanc)

Please help me with this problem. Write an equation that can be used to solve the... (answered by josgarithmetic,macston,MathTherapy)

Could somebody please help me with this question. A rectangle has a length of 35 yards... (answered by josgarithmetic)

Hello, I am having a little trouble with this algebra problem. if someone could be kind (answered by nerdybill)

Please help me solve this problem Equilateral triangle ABC has side lengths 1. Circle... (answered by richard1234)

HI math tutors. I am extremely confused with this if you guys could help me i would... (answered by Alan3354)

Somebody can help solve this problem? a play ground is 101ft longer than it's wide. If (answered by Alan3354)

Hi I'm stuck on this question, I have tried looking at other resources for help and asked (answered by Theo,jim_thompson5910)

I am having trouble with this problem and I was wondering if anyone could help me? I... (answered by orca)