Regular polygons mean all sides are equal and so are all angles. They have a circumcircle with radius and an incircle with radius
A regular polygon can be analyzed easily if we think of it as having been built from isosceles triangles with the unequal side the equal sides and the unequal angle at the center of the circumcircle. Drop the perpendicular from to the base where is the inradius.
With -sided polygon, we have the following relations among these important quantities:
- Area of the
Find the area of a regular decagon with side length
congruent isosceles triangles. So the value of isA regular decagon is composed of
Substituting this into the formula, we have
Note: is in radian.