Triangle formed by lines y=x, x=6, and y=0

To find the area of the triangle formed by the lines y=x, x=6, and y=0, we can follow these steps:

Step 1: Plotting the lines
First, let's plot the given lines on a coordinate plane to visualize the triangle. The lines y=x and y=0 are easy to plot, as they are simple equations representing straight lines. The line x=6 is a vertical line passing through the x-coordinate 6.

The graph should look like this:

```
y
^
|
|
| x=6
| *
| / |
| / |
| / |
| / |
|/ |
|---------|------> x
```

Step 2: Identifying the vertices of the triangle
The triangle is formed by the intersection points of the three lines. To find the vertices, we need to find the points where these lines intersect.

Vertex 1: The line y=x intersects the x=6 line at the point (6,6).
Vertex 2: The line y=0 intersects the x=6 line at the point (6,0).
Vertex 3: The line y=0 intersects the y=x line at the point (0,0).

Step 3: Calculating the base and height of the triangle
To find the base and height of the triangle, we need to determine the length of the line segments connecting the vertices.

The base of the triangle is the horizontal distance between vertex 1 (6,6) and vertex 2 (6,0), which is 6 units.

The height of the triangle is the vertical distance between vertex 2 (6,0) and vertex 3 (0,0), which is 0 units.

Step 4: Calculating the area of the triangle
The area of a triangle can be calculated by using the formula: Area = (base * height) / 2.

In this case, the base is 6 units and the height is 0 units. Therefore, the area of the triangle is:

Area = (6 * 0) / 2 = 0 square units.

Conclusion:
The area of the triangle formed by the lines y=x, x=6, and y=0 is 0 square units.

18 sq units.