# Triangle inscribed in a Hexagon

• Oct 24th 2012, 05:22 PM
gfbrd
Triangle inscribed in a Hexagon
Hey sorry if this is in the wrong place and if the picture is too small but I need some help

What can you say about a triangle that is inscribed in a hexagon, where the vertices of the triangle hits the midpoint of 3 sides of a hexagon?
if there is something about it please explain it to me so I can understand better, thanks.
• Oct 24th 2012, 05:23 PM
Prove It
Re: Triangle inscribed in a Hexagon
I don't see a picture...
• Oct 24th 2012, 05:24 PM
gfbrd
Re: Triangle inscribed in a Hexagon
sorry i just added it right now
• Oct 24th 2012, 05:25 PM
Prove It
Re: Triangle inscribed in a Hexagon
Is it a regular hexagon or an arbitrary hexagon?
• Oct 24th 2012, 05:25 PM
gfbrd
Re: Triangle inscribed in a Hexagon
it is a regular hexagon
• Oct 25th 2012, 10:40 AM
bjhopper
Re: Triangle inscribed in a Hexagon
ABCDEF is aregular hexagon. Name the three midpoints that form the triangle
• Oct 25th 2012, 03:36 PM
Soroban
Re: Triangle inscribed in a Hexagon
Hello, gfbrd!

Quote:

What can you say about a triangle that is inscribed in a regular hexagon,
where the vertices of the triangle are the midpoint of 3 sides of a hexagon?

What do they want me to say?
. . It has three sides.
. . It has three angles.
. . It is equilateral.
. . It has 60o angles.

Okay, I'll get serious . . .

A regular hexagon is composed of six equilateral triangles of side a.
Consider the upper half of the hexagon.
Code:

```            : - - a - - :             *  *  *  *  *           * .        . *         a *  .      .  * a         *=================*         *      .  .      *       *        . .        *       *  *  *  *  *  *  *  *  *       : - - a - - : - - a - - :```
We have an isosceles trapezoid.
The side of the triangle is the median.
Its length is the average of the lengths
. . of the two parallel sides.
Hence, the side of the triangle is $\tfrac{3}{2}a.$

The triangle's perimeter is $\tfrac{3}{4}$ of the hexagon's perimeter.
The triangle's area is $\tfrac{3}{8}$ of the hexagon's area.
• Oct 25th 2012, 04:00 PM
bjhopper
Re: Triangle inscribed in a Hexagon
There are two additional triangles which can be drawn meeting the general requirements
• Oct 25th 2012, 06:53 PM
gfbrd
Re: Triangle inscribed in a Hexagon
Great thanks for your help everyone.
• Nov 1st 2012, 02:01 AM
elisaevedent
Re: Triangle inscribed in a Hexagon
• Nov 8th 2012, 07:19 PM
Chalama123
Re: Triangle inscribed in a Hexagon