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Areas of Regular Polygons  Lesson 115
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 306090 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:
