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 ae 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.

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