Wednesday, July 10

how to find the perimeter of a polygon

In geometry which is a branch of math, there are primarily two types of polygons.
(a) Regular polygons
(b) Irregular polygons

The phrase ‘perimeter of polygon’ refers to the sum of all the sides of a polygon. First let us try to understand how to find the perimeter of a polygon that is irregular.

Perimeter of irregular polygons:

An irregular polygon is the one in which the measure of all the sides of the polygon are unequal. To find the perimeter of such a polygon, there is no other way but to add the lengths of each of the sides. For that the measure of each of the sides has to be known. If the lengths of all the sides of an irregular polygon are not known, then one cannot find its perimeter.

Example 1: Find the perimeter of the following irregular polygon.

In the above polygon all the sides of the polygon are given. Therefore the perimeter would be
= 5 + 4 + 3 + 2 + 6
= 20 inches

Example 2: Now consider the following irregular polygon.

The perimeter of this polygon cannot be found as some of the sides are not known and there is now way by which we can calculate them as well.
Now let us learn to find the perimeter of a polygon that is regular.

Perimeter of regular polygons:

For regular polygons, the formula for finding the perimeter would be as follows:

P = n * a

Here, P = perimeter of the polygon, n = number of sides of the polygon and a = measure of the length of the side of the polygon.

In a regular polygon all the sides are of equal length. Thus if the polygon has n sides each of length a, then the perimeter would be

= a + a + a + a + …. n times
= a * n

Example : Find the perimeter of the polygon below

We see that each of the sides of the given polygon ( an equilateral triangle in this case) is 2 inches. Therefore the perimeter would be,
P = 2 * 3 (because there are 3 sides in the given polygon)
P = 6 inches <- answer="" p="">
In general Area and Perimeter of Polygons have different methods of solution based on whether the polygon is regular or irregular. Usually there are set formulas for area and perimeter of regular polygons. However for irregular polygons there are no well defined formulas and the calculations have to be done using various methods on case to case bases.
In case of irregular polygons, all the sides of the polygon have to be given. If not, then the unknown sides have to be calculable using basic concepts of geometry. Once we find all the sides, then adding them up would give us the perimeter of the irregular polygon.
For finding the area of an irregular polygon, we divide the polygon to rectangles and triangles with known dimensions. Then add up the areas thus found.

No comments:

Post a Comment