https://file.aiquickdraw.com/mathbot/file/1725423681356z0ryukq9.jpg

The image shows a polygon on a coordinate grid, and the question asks to find the perimeter of the polygon using the given vertices. Here's how to solve it:

### Steps to Calculate the Perimeter:

1. **Identify the vertices of the polygon**: From the image, we can see that the vertices are labeled, and their coordinates can be extracted.

2. **Calculate the distance between each pair of consecutive vertices**: This involves using the distance formula:
   \[
   \text{Distance} = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]
   for each pair of consecutive vertices.

3. **Sum all the distances**: Adding up all the distances calculated in the previous step will give the perimeter of the polygon.

### Let’s extract the coordinates and calculate:

From the image, the coordinates of the polygon vertices appear to be:
- \( A = (2, 2) \)
- \( B = (5, 2) \)
- \( C = (5, 5) \)
- \( D = (7, 5) \)
- \( E = (7, 1) \)
- \( F = (2, 1) \)

### Calculate the distances between consecutive points:

1. \( AB \) distance:
   \[
   \sqrt{(5 - 2)^2 + (2 - 2)^2} = \sqrt{3^2 + 0^2} = \sqrt{9} = 3
   \]

2. \( BC \) distance:
   \[
   \sqrt{(5 - 5)^2 + (5 - 2)^2} = \sqrt{0^2 + 3^2} = \sqrt{9} = 3
   \]

3. \( CD \) distance:
   \[
   \sqrt{(7 - 5)^2 + (5 - 5)^2} = \sqrt{2^2 + 0^2} = \sqrt{4} = 2
   \]

4. \( DE \) distance:
   \[
   \sqrt{(7 - 7)^2 + (1 - 5)^2} = \sqrt{0^2 + 4^2} = \sqrt{16} = 4
   \]

5. \( EF \) distance:
   \[
   \sqrt{(2 - 7)^2 + (1 - 1)^2} = \sqrt{5^2 + 0^2} = \sqrt{25} = 5
   \]

6. \( FA \) distance:
   \[
   \sqrt{(2 - 2)^2 + (2 - 1)^2} = \sqrt{0^2 + 1^2} = \sqrt{1} = 1
   \]

### Total Perimeter Calculation:
\[
3 + 3 + 2 + 4 + 5 + 1 = 18 \text{ units}
\]

The perimeter of the polygon is **18 units**.

Would you like more details or have any other questions?

### Related Questions:
1. What is the general formula for the perimeter of a polygon with \(n\) vertices?
2. How does the distance formula work in a 3D coordinate system?
3. Can you calculate the perimeter of a regular polygon given the length of one side?
4. What are some real-life applications of calculating the perimeter of polygons?
5. How can you calculate the area of the polygon given these vertices?

### Tip:
When working with coordinate grids, always double-check the coordinates you extract from the graph to ensure accuracy in your calculations.

Find the perimeter of the polygon with the given vertices. Round your answer to the nearest hundredth.

Learn how to calculate the perimeter of a polygon using coordinate geometry. This problem involves identifying the vertices, applying the distance formula between consecutive points, and summing these distances. Suitable for students in Grades 7-9.

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