As usual, I've provided my solution to this geometry problem below...We've got plenty to work with from the problem above, even if it doesn't seem like it at first. I started by drawing my hexagon on paper. I did not, however, use a ruler, so my unit squares don't exactly look identical!
|Click the picture to make it bigger!|
I labeled my outer vertices A through F, and then I gave the corners of the triangle labels as well. Then I started to look at angles. I used red to start describing the angle AGB.
And here, you can see my math. I found the angle AGB and divided by two to find angle AGJ, a right triangle at the top of our hexagon. Then, I used basic trigonometry and the hypotenuse of that triangle to find the length between points A and J of the hexagon.
From there, it was easy to determine the perimeter of the hexagon.
Any questions about my work? Did you solve the problem a different way? Please let us know in the comments!