Geometry

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# Perimeter of a Pentagon

## The Perimeter Formulas

There are two formulas for finding perimeter of a pentagon.

For a regular pentagon where all sides are the same length, the formula is given as:**P = 5s**

Where *P* is the perimeter and *s* is the side length.

For an irregular pentagon where the sides are not all the same length, the formula is given as:**P = a + b + c + d + e**

Where *a* → *e* are the lengths of each side.

### Example Problems

Problem 1:

Find the perimeter of a regular pentagon with a side length of 15.

Solution:

Since we know this is a regular pentagon, we can plug the side length 15 into the regular pentagon formula.

P = 5s

P = 5(15) = 75**The perimeter is 75.**

Problem 2:

In irregular pentagon has side lengths a = 2.36, b = 4.01, c = 3.12, d = 3.22, and e = 4.41. What is the perimeter?

Solution:

Let’s plug the side lengths into the irregular pentagon formula.

P = a + b + c + d + e

P = 2.36 + 4.01 + 3.12 + 3.22 + 4.41 = 17.12**The perimeter is 17.12.**