The N Sided Polygon Formula: A Comprehensive Guide For 2023
Are you struggling to understand the n sided polygon formula? Look no further! This guide will provide you with everything you need to know about this mathematical concept in a relaxed, easy-to-understand language.
What is an n sided polygon?
A polygon is a flat, two-dimensional shape with straight sides. An n sided polygon is a polygon with n number of sides. For example, a triangle is a three-sided polygon, a square is a four-sided polygon, and a pentagon is a five-sided polygon.
What is the n sided polygon formula?
The n sided polygon formula is used to calculate the interior angles of a regular n-sided polygon. The formula is:
Interior angle = (n-2) x 180 / n
Let's break down this formula. The "n" represents the number of sides in the polygon. The "-2" is subtracting the two exterior angles of the polygon to calculate the interior angle. The "180" is the sum of all of the interior angles in a polygon, and the "/n" divides that sum by the number of sides in the polygon.
How to use the n sided polygon formula
Let's use the formula to calculate the interior angle of a regular hexagon, which is a six-sided polygon. We plug in "n=6" into the formula:
Interior angle = (6-2) x 180 / 6 = 120 degrees
Therefore, the interior angle of a regular hexagon is 120 degrees.
What is a regular polygon?
A regular polygon is a polygon with all sides and angles equal. In other words, all of the interior angles are the same, and all of the sides are congruent.
How to find the exterior angle of a regular polygon
The exterior angle of a polygon is the angle formed by one side of the polygon and the extension of an adjacent side. The exterior angle of a regular polygon can be calculated using the following formula:
Exterior angle = 360 / n
Let's use the formula to calculate the exterior angle of a regular octagon, which is an eight-sided polygon:
Exterior angle = 360 / 8 = 45 degrees
Therefore, the exterior angle of a regular octagon is 45 degrees.
What is the sum of the interior angles of a polygon?
The sum of the interior angles of a polygon can be calculated using the following formula:
Sum of interior angles = (n-2) x 180
Let's use the formula to calculate the sum of the interior angles of a decagon, which is a ten-sided polygon:
Sum of interior angles = (10-2) x 180 = 1440 degrees
Therefore, the sum of the interior angles of a decagon is 1440 degrees.
What is the exterior angle sum of a polygon?
The exterior angle sum of a polygon is always 360 degrees. This means that if you add up all of the exterior angles of a polygon, the sum will always be 360 degrees.
What is the difference between a regular polygon and an irregular polygon?
A regular polygon has all sides and angles equal, while an irregular polygon has sides and angles that are not equal. For example, a rectangle is an irregular polygon because it has two sets of congruent sides and two sets of non-congruent sides.
How to find the apothem of a regular polygon
The apothem of a regular polygon is the distance from the center of the polygon to the midpoint of a side. The apothem can be calculated using the following formula:
Apothem = (s/2) x tan(180/n)
Where "s" is the length of one side of the polygon, and "n" is the number of sides in the polygon.
Conclusion
The n sided polygon formula is a crucial concept in mathematics. It allows us to calculate interior and exterior angles, as well as the apothem and sum of angles of regular polygons. With this guide, you should now have a better understanding of the n sided polygon formula and how to use it.
Remember, practice makes perfect! Make sure to practice using the n sided polygon formula with different regular polygons to improve your understanding of this concept.
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