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apothem of a regular polygon
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A regular polygon has equal side lengths. As a result you can use the length of one of the sides in order to calculate the length of the apothem.

Apothem length formula from side length equals. 

n= number of sides
tan = tangent function in degrees
s = side length

If you don’t know the length of one side of a regular polygon, but do know the radius you can still find the apothem using radius and the following formula.

r = radius
cos = cosine in degrees
n = number of sides of the regular polygon.

apothem from side length s/2tan(180/n)
apothem formula from radius r cos(180/n)
Definition: A line segment from the midpoint of a side to the center of a regular polygon.

•Exterior angles of regular polygons equal 360/ Number of sides

• Interior angle formula 


Transcript Regular Polygons
Welcome to MooMooMath. Today we are going to talk about regular polygons. Let’s first look at some pictures to see which are and which aren’t regular polygons. So the definition of a regular polygon is a polygon in which all sides are congruent. (Congruent just means equal) and congruent angles. So here are a couple pictures and I’m going to mark these. OK if these sides are the same then the angles have to be same. If these three sides are the same then the angles will be the same. On this hexagon if the six sides are the same then the 6 angles must be the same. Again it must have congruent sides and congruent angles. So let’s look at our pictures here Ok this first one has 4 right angles and 4 marked sides so yes it is a regular polygon. Let’s look at the second one, has four right angles, but it only has these two sides of 5 and these two sides of 7 so this one is not a regular polygon because the sides are different. Now let’s look at the third one here. We have all 5 sides the same, but notice we have an acute angle here and an obtuse angle here and a really large angle here, so these angles are not the same so this one here is not a regular polygon. So the only perfect one in the bunch is this one here (Circles the square) So the other key thing to look for with the angles, you never have want to have a concave figure (concave is a figure that caves in) If it had been a convex figure and all the sides are the same then all the angles would have been the same. Hope this video was helpful.

Regular polygon shapes

N = Number of sides
Measure interior exterior angles regular polygon
Exterior angle:

360/n = measure of exterior angle, 

n is the number of sides of a regular polygon.

Ex. n = 5 so 360/5 = 72 degrees

Interior angle:
Method 1. Use the Interior Angle Formula

​      n
n = number of sides of the polygon

Step 1

Step 2

Step 3
Find the interior and exterior angles of a regular polygon with 5 sides.
triangle square hexagon
pentagon octagon decagon
Equilateral Triangle

For a complete list of the names of polygons see this link

Common examples of regular polygons

Regular Polygon Angles

Method 2

Find the exterior angle using 360/n formula, then subtract from 180.  

Why? Interior and exterior angles of a
regular polygon are linear pairs (supplementary).

Step 1.  360/5 = 72 

Step 2. 180 - 72 = 108 degrees 

Apothem and regular polygons

A regular polygon has these additional traits.

•all sides are congruent  

•all angles are congruent

Congruent just means they are equal and is represented with the 
Symbol ≅
Use the interior angle formula in order to find the measure of one interior angle of a regular polygon​
A regular polygon is simply a polygon that has some additional traits. A polygon is closed figure created with line segments. In other words there are not any curves in a polygon. A square,rectangle, and triangles are all examples of polygons. .