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Day 119: Area of a Regular Polygon

Call me old fashioned, but I think the derivation for the area of a regular polygon formula is one of the most amazing aspects of high school level Euclidean geometry. It encompasses so much knowledge - it marks the the point when everything we've been learning finally comes together.

Which is exactly the reason why the students HATE this unit.

Worst of all, most of the content that students need to get through this unit (as well as most of 2nd semester) came from 1st semester, and too many students have the "out of sight, out of mind" philosophy when it comes to the semester breakdown. It all gets back to the fixed vs. growth mindset ideas, but SBG throws a nice wrinkle into the mix. I finally settled on just saying that students will be assumed to be proficient on ALL standards covered in 1st semester. So if you need to know how to use Pythagorean Theorem to solve for the missing side of a kite, then it's on you. I will still give a proficient score of 2 (the passing line) to students who can demonstrate the proper setup (showing that the diagonals of a kite for a right angle) even if they can't solve it.

In any event, I work through the discovery for the area of a regular polygon (how about AoRP from now on?) on my tablet as a derivation that the students are expected to follow. By the end, they're exasperated and are hoping that there's a shortcut that I just didn't show them at first (they know that is something I would totally do). Unfortunately, the only "shortcut" (after the central angle, right triangle trig, interior triangles and multiplication) is to catch the perimeter popping out. The students are generally upset that they'll be expected to do all that work for just ONE problem. Babies.

One pleasant surprise was how many students still have their laminated trig tables that I gave them back in 1st semester AND they have a basic memory of how to use them. Awesome!
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