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Areas of Regular Polygons - Lesson 11-5

Today we started by deriving a formula for the area of an equilateral (regular) triangle. If you start with an equilateral triangle with side length s: And then do the standard procedure for finding the length of the altitude (love those 30-60-90 triangles!), you are then able to use the formula for the area of a triangle to derive a new formula which can be summarized as follows: Next, we can generalize an area formula for all regular polygons. To start, we need to define the radius and the apothem of a regular polygon: If we look at a pentagon, you should be able to see how the formula for its area would be as shown in the table below:  The same can be said for an octagon  and a dodecagon.  In conclusion, we can derive the general formula to find the area of any given regular polygon: Other Links  Class Notes Lesson 11-1 Lesson 11-2 Lesson 11-3 Lesson 11-4 Quiz Topics Lesson 11-5 Lesson 11-6 Lesson 11-7 Lesson 11-8 Test Topics    If you have questions, email me at baroodyj@doversherborn.org