The task in the image is to write an expression for calculating the perimeter of the polygon shown in the diagram.

Analysis:

The given polygon is a hexagon, and its sides are marked with two variables:

• Some sides are labeled $a$, and others are labeled $b$.
• Each side is clearly defined, and there are 3 sides labeled $a$ and 3 sides labeled $b$.

Solution:

The perimeter of a polygon is the sum of the lengths of all its sides. In this case: $\text{Perimeter} = a + a + a + b + b + b = 3a + 3b.$

Final Expression:

$\text{Perimeter} = 3a + 3b$

This expression gives the total perimeter of the hexagon.

Would you like me to clarify this further or provide step-by-step calculations? Let me know if you have specific questions!

Related Questions:

1. How do you calculate the perimeter of polygons with unequal side lengths?
2. What is the perimeter formula for a regular hexagon?
3. How does the concept of perimeter relate to the area of a polygon?
4. Can this expression $3a + 3b$ be simplified further using factoring?
5. How would you calculate the perimeter if the values of $a$ and $b$ were given?

Tip:

When calculating the perimeter of a polygon, always ensure that all sides are properly accounted for and labeled to avoid errors.