To find the total perimeter of the pentagon-shaped chicken pen, we need to understand that the perimeter of any polygon is the sum of the lengths of all its sides.
In this case, the pentagon has 5 equal sides, and each side is [tex]\(3\sqrt{5}\)[/tex] yards long.
To calculate the perimeter, we multiply the length of one side by the number of sides.
Let's break it down step by step:
1. Identify the length of one side:
The length of one side is [tex]\(3\sqrt{5}\)[/tex] yards.
2. Calculate the number of sides:
A pentagon has 5 sides.
3. Multiply the length of one side by the number of sides:
[tex]\[
\text{Perimeter} = 5 \times 3\sqrt{5}
\][/tex]
4. Perform the multiplication:
[tex]\[
\text{Perimeter} = 15\sqrt{5} \text{ yards}
\][/tex]
Therefore, the total perimeter of the chicken pen is [tex]\(15\sqrt{5}\)[/tex] yards.
Thus, the correct answer is:
B. [tex]\(15\sqrt{5}\)[/tex] yards
