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.