How To Find Perimeter Of A Polygon
The perimeter of a polygon is the total distance of the boundary of the polygon. It is the sum of all the sides of a polygon. In geometry, the perimeter of any 2D shape or figure is defined as the total length of its boundary. The perimeter of a 2D shape is calculated by adding the length of all the sides or the edges enclosing the shape. It is measured in linear units of measurement like inches, feet, meters, centimeters, etc.
Polygon and Its Types
A polygon is a plane flat, two-dimensional closed shape bounded with straight sides. If any side is curved, it is not a polygon. The points where two sides meet are the vertices (or corners) of a polygon. There are two types of polygons:
- Regular Polygons: A polygon that has equal sides as well as equal interior angles is known as a regular polygon. Examples include an equilateral triangle and a square.
- Irregular Polygons: A polygon that is neither equilateral nor equiangular is known as an irregular polygon. Examples include a rectangle and a scalene triangle.
Perimeter Calculation
The perimeter of a polygon is the total length of all sides of a polygon. To find the perimeter, ensure that all the side-lengths have the same unit. If the lengths of sides are given in different units, then first convert them to the same unit. Finally, add lengths of all sides to find the perimeter.
Difference between Area and Perimeter of a Polygon
The area of a polygon is the region bounded within the sides of the polygon, while the perimeter of a polygon is the total length of its boundary. The area of polygons is expressed in square units like $in^{2},\; ft^{2},\; m^{2},\; cm^{2}$, etc. The perimeter is expressed in linear units like in, ft, m, cm, etc.
Perimeter of Regular Polygons
In regular polygons, the length of each side is the same. To find the perimeter, simply multiply the side-length by the number of sides. For example, the perimeter of a regular hexagon is calculated by multiplying the number of sides by the length of one side.
Perimeter of Irregular Polygons
To calculate the perimeter of irregular polygons, add the lengths of all sides of the polygon.
Perimeter of Polygon Using Coordinates of Vertices
The perimeter of a polygon can be found if the coordinates of the vertices are given using the distance formula. Find the lengths of sides using the distance formula and then identify the type of the polygon (regular or irregular) based on the dimensions to find the perimeter.
Conclusion
In conclusion, we have learned about the perimeter of a polygon and formulas to find the perimeter of regular and irregular polygons. The perimeter of a polygon is an important concept in geometry and has practical applications in various fields.
Frequently Asked Questions on Perimeter of a Polygon
1. Is the perimeter of a regular polygon directly proportional to the length of its side?
Yes, the perimeter of a regular polygon is directly proportional to the length of its side. The perimeter of a regular polygon is calculated by multiplying the number of sides by the length of one side.
2. What is the formula to calculate the perimeter of an isosceles triangle?
An isosceles triangle has two sides equal. If two equal sides are of measure l and the base is b, then the perimeter of the isosceles triangle is given by l + l + b or 2l + b.
3. Can the perimeter of a square be greater than its area?
No, the area of a square is always greater than its perimeter. The area of a square is given by $(side)^{2}$, and its perimeter is given by 4(side).
4. Are the perimeters of regular polygons always even?
No, the perimeter of a regular polygon can be odd as well as even. The perimeter of a regular polygon with an even number of sides will always be even. The perimeter of a regular polygon with an odd number of sides can be odd or even depending on the length of the side.
5. How do you find the perimeter of a regular polygon with n sides?
To find the perimeter of a regular polygon with n sides, multiply the length of one side by n. The formula for the perimeter of a regular polygon is Perimeter = n × (length of a side).
6. How to find the perimeter of a polygon?
To find the perimeter of a polygon, add all the sides of the polygon to find its perimeter.