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To find the perimeter of the polygon with vertices \( L(1, 4) \), \( N(2, 0) \), \( M(4, 0) \), and \( P(-1, -2) \), we need to:

1. Calculate the lengths of the sides of the polygon using the distance formula:
   \[
   d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}
   \]
   for each pair of adjacent vertices.

Let's calculate the distances between the following pairs of points:

- \( L(1, 4) \) and \( N(2, 0) \)
- \( N(2, 0) \) and \( M(4, 0) \)
- \( M(4, 0) \) and \( P(-1, -2) \)
- \( P(-1, -2) \) and \( L(1, 4) \)

I'll now compute these distances and sum them to find the perimeter.The perimeter of the polygon is approximately \( 17.83 \) units when rounded to the nearest hundredth.

Would you like further details on the calculations or have any questions?

Here are 5 related questions for further exploration:
1. How do you calculate the area of this polygon using the coordinates?
2. What is the significance of rounding in perimeter calculations?
3. How can you determine whether the polygon is a specific type (e.g., quadrilateral)?
4. Can the perimeter be affected if the polygon were in 3D space?
5. What would happen to the perimeter if one of the vertices was shifted?

**Tip:** Always double-check your units when working with geometry, especially when dealing with coordinate-based 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 with vertices L(1, 4), N(2, 0), M(4, 0), and P(-1, -2) using the distance formula. The perimeter is approximately 17.83 units. Ideal for students in Grades 8-10, this problem focuses on geometry and the application of coordinate systems.

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