How to calculate the apothegm of a regular polygon?

The apothegm is the sum of the areas of all the triangles that can be constructed by extending the sides of the polygon It can be easily shown that the sum of the areas of all the triangles with the same base is equal to the area of the polygon. Let’s say that we have a regular polygon with sides of length a. Its area is equal to A = π a2. The area of a triangle with base equal to a side of the poly

How to calculate the apothe

If the regular polygon has an even number of sides, the sum of the internal angles is equal to 360°. The sides of a regular polygon are in the ratio 1:1:1:…:n, where n is the number of sides. The sum of the internal angles is equal to a half of the sum of the angles around the polygon. This means, that we have to find the sum of the angles by adding up all the angles between adjacent sides of the poly

How to calculate the apothegm of a 5-sided polygon?

There are two types of regular 5-sided polygons. You have a star pentagon and a pentagon. A star pentagon has five equilateral triangles connected at the corners and shares the same vertex with each of the triangles. A pentagon has five equilateral internal angles. If you have a regular pentagon, the sum of the measures of its internal angles is 180 degrees. A star pentagon is a regular pentagon whose opposite sides have been truncated. While it does not have

How do you calculate the apothegm of a pentagon with a side of 5?

If you want to calculate the area of a regular pentagon, start by drawing a line segment with length equal to the length of one side of your pentagon. Now, draw two more line segments, each with length equal to half the length of the first segment, and connect them to the opposite corners of the pentagon. The area of a regular pentagon with a side of 5 is the area of a regular pentagon with four sides with length equal to the length of the first line segment

How to calculate the apothegm of a regular pentagon?

The area of a regular pentagon is equal to (1/2) base × height × sin 30°, where the base is the length of one side and the height is the length of the altitude. The length of the altitude is half the length of the diagonal of a regular pentagon. Using the Pythagorean theorem, you can easily see that the length of the diagonal is equal to the square root of five times the area of a regular pentagon.