The perimeter of a geometric figure is the sum of the lengths of its sides. The perimeter of the pentagon​ (five-sided figure) on the right is 36 centimeters.
a. Write an equation for perimeter.
b. Solve the equation in part​ (a).
c. Find the length of each side.

Let's solve the problem step by step.

### Part (a): Write an equation for the perimeter.
Given that the perimeter of a pentagon is the sum of the lengths of its sides, if each side of the pentagon is of equal length, then let the length of each side be denoted by \( s \). The perimeter \( P \) of the pentagon is given by:

\[
P = 5s
\]

Since we are given that the perimeter is 36 centimeters, we can write the equation:

\[
5s = 36
\]

### Part (b): Solve the equation.
To find the length of each side \( s \), we solve the equation \( 5s = 36 \):

\[
s = \frac{36}{5} = 7.2 \text{ centimeters}
\]

### Part (c): Find the length of each side.
From part (b), we found that the length of each side of the pentagon is:

\[
s = 7.2 \text{ centimeters}
\]

So, each side of the pentagon is 7.2 centimeters long.

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Do you want any details or have any questions? Here are some related questions:

1. What is the formula for the perimeter of a regular hexagon?
2. How would the equation change if the pentagon had sides of different lengths?
3. If one side of the pentagon was extended by 2 cm, what would the new perimeter be?
4. What would be the side length if the perimeter was 50 cm?
5. How can you determine the perimeter of a pentagon with given side lengths?
6. If the side length was doubled, what would be the new perimeter?
7. How does the formula change if you only know the perimeter but not the number of sides?
8. How does perimeter calculation change for irregular polygons?

**Tip:** When solving equations involving perimeter, always ensure the correct number of sides is considered. For a pentagon, the perimeter is the sum of five sides.

Learn how to calculate the perimeter of a pentagon with sides of equal length. Step-by-step solution provided with detailed equation writing and solving. Each side of the pentagon is determined to be 7.2 centimeters. Suitable for students in Grades 7-9.

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