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Tuesday, May 26, 2015

Problem of the Week

Happy Tuesday from the Center of Math team! Our Problem of the Week is coming to you one day later than usual because we celebrated Memorial Day yesterday. Here's the problem, which we posted on our Facebook, Twitter, and Google+ accounts just a little while ago:

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!
-Tori