There is a real appeal to solving Algebra through Geometry!
The students came up with three or four different methods of their own (using string and chalk on the blacktop) - I particularly liked this one!
Both of these are, as far as I know, original drawings.
Quite chuffed that, after years of learning from books, I am developing a capacity to work this stuff out for myself!
I am sure that, in terms of world knowledge, this is not a new discovery, but the formula given above for the area of any regular polygon is something I was searching for and was able to come to by myself!
(. . . but I am still working on a formula for the radius of the incircle)
Also quite clear from the above that similar triangles with 1/2 length edges have 1/4 the area.
The following are developed from an excellent little paper I found here!
Table so useful I am posting a blank for you to play with in the "Downloads" section here!
I was initially quite excited by the 100, 75, 125 triangle and went straight into construction without realizing that these proportions would reduce to something already very familiar . . . . .
. . . . but in doing so discovered that standard U.S. Letter sized paper is a basic Pythagorean Triangle with an even 1/2" margin - who knew?
