10.6. Area and Perimeter of Regular Polygons http://www.ck12.org
Apothem:A line segment drawn from the center of a regular polygon to the midpoint of one of its sides.
We could have also said that the apothem is perpendicular to the side it is drawn to. By the Isosceles Triangle
Theorem, the apothem is the perpendicular bisector of the side of the regular polygon. The apothem is also the
height, or altitude of the isosceles triangles.
Example 3:Find the length of the apothem in the regular octagon. Round your answer to the nearest hundredth.
Solution:To find the length of the apothem,AB, you will need to use the trig ratios. First, findm^6 CAD. There are
360 ◦around a point, som^6 CAD=^360
◦
8 =^45◦. Now, we can use this to find the other two angles in 4 CAD.m (^6) ACB
andm^6 ADCare equal because 4 CADis a right triangle.
m^6 CAD+m^6 ACB+m^6 ADC= 180 ◦
45 ◦+ 2 m^6 ACB= 180 ◦
2 m^6 ACB= 135 ◦
m^6 ACB= 67. 5 ◦
To findAB, we must use the tangent ratio. You can use either acute angle.