Formulas for Regular Polygons
Regular polygons are two-dimensional closed figures with finite straight lines, as we have explained. It is made up of straight lines that join. The formulas used in a regular polygon are listed below.
Regular Polygon Area Formula
The region that the regular polygon occupies is known as its area. A polygon is classified as a triangle, quadrilateral, pentagon, etc. based on how many sides it has. The regular polygon’s area is determined by
Area of Regular Polygon (A) = [l2n]/[4tan(π/n)] units2
where,
- l is the side length
- n is the number of sides
Example: Determine the area of a polygon with 5 sides and a side length of 5 centimeters.
Solution:
Given,
- n = 5 cm
- l = 5 cm
Method for determining the region is,
A = [l2n]/[4tan(π/n)]
A = [52 x 5] / [4 tan(180/5)]
A = 125 / 4 x 0.7265
A = 43.014 cm2
Thus, the area of the polygon with five(5) sides is 43.014 cm2
How to Calculate Area of a Regular Polygon?
The area of a regular polygon is calculated using the steps discussed below,
Step 1: Mark the length of each side and the number of the sides of given regular polygon.
Step 2: Use the area of the regular polygon formula discussed above with the values from Step 1.
Step 3: Simplify the values from Step 2 to find the required area of the given polygon.
Regular Polygon Perimeter Formula
A regular polygon’s perimeter may be calculated using a simple formula. The perimeter (P) of a regular polygon with n sides and s sides may be computed by applying the formula below:
Perimeter (P) = n × s
where,
- n is number of Sides in a Regular Polygon
- s is length of the side of Regular Polygon
Example: Find the perimeter of the hexagon with a length of 7 cm.
Solution:
Given,
Length of Side = 7 cm
For Hexagon,
n = 6
Perimeter of Regular Polygon(P) = n × s
P = 6 × 7 = 42 cm
Thus, the perimeter of the hexagon is 42 cm
Regular Polygon
Regular polygons are closed two-dimensional planar figures constructed entirely of straight lines. In contrast to a regular polygon, which is made up of solely straight lines of equal length, an irregular polygon has varied sides and angles. Polygons are two-dimensional geometric shapes with a fixed number of sides.
The sides or edges of a polygon are formed by linking end-to-end segments of a straight line to form a closed shape. The intersection of two line segments that result in an angle is referred to as a vertex or corner. A polygon is referred to be a regular polygon if its sides are congruent.
Table of Content
- Regular Polygon Definition
- Equilateral Triangle
- Square
- Regular Pentagon
- Regular Hexagon
- Regular Heptagon
- Regular Octagon
- Properties of Regular Polygons
- Formulas for Regular Polygons
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