Last modified on April 22nd, 2021

Perimeter of a Polygon

The perimeter of a polygon is the sum of the lengths of all four sides of the polygon. The unit of perimeter is same as the unit each side of the polygon.

Since a polygon can be both regular and irregular; we use different approaches for finding their areas. Let us study each one of them in detail. 

How to Find the Perimeter of a Regular Polygon

All sides of a regular polygon being equal in length, we can obtain its perimeter by repeated addition of each of its side. The perimeter of a regular polygon with n sides can be determined using the following formula:

Perimeter of Regular Polygon

Find the perimeter of a regular polygon having four sides, each measuring 12 cm.

Solution:

As we know,
Perimeter (P) = n x s, here n = 4, s = 12 cm
= 4 x 12 cm
= 48 cm

Find the perimeter of a regular polygon having six sides, each side measuring 4.5 m.

Solution:

 As we know,
Perimeter (P) = n x s, here n = 6, s = 4.5 cm
= 6 x 4.5 m
= 27 m

How to Find the Perimeter of an Irregular Polygon

Irregular polygon being consists of unequal sides; its perimeter is obtained by simply adding all the sides of the polygon. The formula is given below:

Perimeter of Irregular Polygon

Find the perimeter of an irregular polygon with sides measuring 6 cm, 9 cm, 10 cm and 5 cm.

Solution:

As we know,
Perimeter (P) = sum of all the sides around the polygon
= (6 + 9 + 10 + 5) cm
= 30 cm

Find the perimeter of a four sided irregular polygon with two adjacent sides measuring 6 m and 16 m respectively. Also consider that the two opposite sides of the polygon are equal.

Solution:

Since the opposite sides of the given polygon are equal, two of its sides measure 6m and the other two measure 16 m
Now, as we know,
Perimeter (P) = sum of all the sides around the polygon, here side 1 = side 3 and side 2 = side 4
Thus the formula for this polygon becomes,
P = 2(side 1 + side 2), here side 1 = 6 m, side 2 = 16 m
= 2(6 + 16) m
 = 44 m

Finding the Perimeter of Some Common and Basic Polygons

If we are looking to find the perimeter of basic polygons such as triangle, rectangle, parallelogram, rhombus, trapezoid, kite, pentagon, and hexagon, we can also use their standard formulas that are given below:

Perimeter of Polygon

Finding the Perimeter of a Polygon Given on a Coordinate Plane

For determining the area of a polygon given on a coordinate plane, we will use the distance formula to determine the lengths of all its sides, adding the lengths will give the perimeter of the polygon.

Steps to Follow

  1. Plot the given coordinates
  2. Connect the dots to form the figure
  3. Determine the lengths of its sides by using the distance formula given below:

d = (x2 – x1)2 + (y2 – y1)2

See the below given link for an example.

Mathbitsnotebook.com

Last modified on April 22nd, 2021

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