How To Find The Perimeter Of A Polygon

Calculating the perimeter of a polygon is a major part high school curriculum, just as are other shapes. However, compared to other shapes, the polygon isn’t a name that is so common. While the rectangle, square, Triangle and Circle are very popular shapes that can be recognised, pointing out a polygon may be confusing. This confusion is actually because the polygon in itself is not a particular r shape. Polygon is simply an umbrella term for a number o shapes, including the very popular ones.

The Square, Rectangle, Tangle and Trapezoid are all Polygons. These shapes all have one thing, which is;

They are 2-dimensional and have at least three sides.

The square shape, for example, has four sides, and so do the rectangle and trapezoid. Triangles only have three sides, irrespective of the form or type. All of these shapes are all polygons. The circle is not a polygon as it does not have sides despite being 2-dimensional.

What is a Polygon?

A polygon is a shape that is 2 dimensional in nature, has sides made of straight lines and is closed (each line connects to each other). The circle cannot be a Polygon as it does not have sides.

There ae two major types of Polygon; The Regular Polygon and the Irregular Polygon

Regular Polygon

The Regular Polygon is one with all sides equal. The square shape has four equal sides and as such, is a regular polygon. A triangle with 3 equal sides also qualifies as a regular polygon.

Irregular Polygon

The irregular polygon is a polygon with at least one unequal side. Most 2 dimensional shapes are irregular polygons. The rectangle, trapezoid and tangles with at least one unequal side are irregular polygons.

Perimeter of A Polygon Formula

The perimeter of a Polygon is the sum of all its sides. This means that the summation of the sides of all polygons will give their perimeter. However, the regular polygon has a formula for easy computation due to the equality of the lengths.  

The perimeter of the regular polygon is denoted as;

P = L x number of sides.

Where;

L = one of the side lengths. Since all the lengths are equal, only one of them is needed

Number of sides represents the total number of sides of the shape. Therefore, if the total number of sides is 4, it will have to be written like that in the formula.

How to Calculate the Perimeter of a Regular Polygon?

Step 1: Confirm whether the Polygon lengths or sides are equal

Step 2: since all of the sides are equal in measurement, pick the value and multiply by the entire number of lengths

How to Calculate the Perimeter of an Irregular Polygon?

Step 1: Confirm whether the polygon sides are not equal

Step 2: Add all of the lengths together to get the shape’s perimeter.

Calculating Polygons with examples.

Now, it is important to know that all polygons have their respective formulas for finding their perimeter. At worst, they can be determined by summing up all sides for an answer.

Example 1

Find the perimeter of the regular polygon below.

Solution

The above diagram is a square as all sides have an equal length of 5. While the square has its perimeter formula, we will use the formula for computing the perimeter of a regular polygon.

P = L x Number of Sides

P = 5 x 4 cm

P = 20 cm

The formula for calculating the above square is consistent for all regular polygons.

Example 2

Consider the rectangle below and calculate its perimeter.

Solution

Based on the shape and the sides, it is obvious that the rectangle is an irregular polygon which is in line with what we have already stated before.     

We will use the second formula, which requires adding all of the side lengths together. The sides are

14 cm, 6 cm, 14 cm, 6 cm

As such, the perimeter of the polygon will be;

P = 14 cm + 6 cm + 14 cm + 6 cm

P = 40 cm.

It is important to note that this same pattern of calculating an irregular polygon, be triangle or trapezoid, also work quite well for the regular polygon. In our first example, the perimeter of the square with equal sides of 5 cm is 20 cm. using this summing up formula will give us;

Perimeter of the square I example 1 = 5 cm + 5 cm + 5 cm + 5cm

Perimeter = 20cm

Obviously, the derived answer is the same as that of the polygon.

Conclusion

The polygon is a simple umbrella term for 2-dimensional shapes with sides of enclosed straight lines. As outlined in this article, computing the perimeter for both the regular and irregular polygon s quite easy. All you need to do is follow the formula and logic implemented in this article.