https://file.aiquickdraw.com/mathbot/file/1726461436684jm8nytyi.jpg

The shape formed by the equations in the image is a **rectilinear polygon** that consists of straight horizontal and vertical line segments. More specifically, it's an enclosed shape resembling a **rectangular L-shape** on the Cartesian plane, with both horizontal and vertical components.

The given equations correspond to line segments, with domain and range restrictions, defining the boundaries of the shape. Here’s a breakdown of the segments:

1. **\( y = -15 \) for \( 4 \leq x \leq 20 \)**: A horizontal line segment at \( y = -15 \), between \( x = 4 \) and \( x = 20 \).
2. **\( y = -4 \) for \( 4 \leq x \leq 15 \)**: A horizontal line segment at \( y = -4 \), between \( x = 4 \) and \( x = 15 \).
3. **\( x = 4 \) for \( -15 \leq y \leq -4 \)**: A vertical line at \( x = 4 \), between \( y = -15 \) and \( y = -4 \).
4. **\( x = 15 \) for \( -10 \leq y \leq -4 \)**: A vertical line at \( x = 15 \), between \( y = -10 \) and \( y = -4 \).
5. **\( x = 20 \) for \( -15 \leq y \leq -10 \)**: A vertical line at \( x = 20 \), between \( y = -15 \) and \( y = -10 \).
6. **\( y = -10 \) for \( 15 \leq x \leq 20 \)**: A horizontal line at \( y = -10 \), between \( x = 15 \) and \( x = 20 \).

These line segments together form an L-shaped polygon. Would you like a more detailed analysis of the equations or any specific calculations regarding the area or perimeter of this shape?

### Relative Questions:
1. How can we calculate the perimeter of this L-shaped polygon?
2. How do we compute the area enclosed by this shape?
3. What are the coordinates of the vertices of the polygon?
4. How do horizontal and vertical line equations differ in their general form?
5. Can this shape be classified as a standard geometric figure?

**Tip**: In mathematics, domain and range restrictions are used to define specific segments of a line instead of the entire line on a graph.

Explore the rectilinear L-shaped polygon formed by line equations with domain and range restrictions. This problem involves understanding horizontal and vertical line equations and how to interpret the boundaries of a shape on a Cartesian plane. Ideal for students in Grades 9-11 studying coordinate geometry.

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