Sketch the region enclosed by the lines x=0, x= 6, y = 2, and y = 6.

Question

Find the area of the region.

Answer 1

Here is the sketch of the region:

```
| |
| |
------|-----|------ y = 6
| |
| |
------|-----|------ y = 2
| |
| |
x = 0 x = 6
```

To find the area of this region, we can divide it into two rectangles:

```
| |
| |
------|-----|------ y = 6
| |
| |
------|-----|------ y = 4
| |
| |
x = 0 x = 6

| |
| |
------|-----|------ y = 4
| |
| |
------|-----|------ y = 2
| |
| |
x = 0 x = 6
```

The first rectangle has a width of 6 and a height of 2, so its area is:

```
6 * 2 = 12
```

The second rectangle has a width of 6 and a height of 2, so its area is:

```
6 * 2 = 12
```

Therefore, the total area of the region is:

```
12 + 12 = 24
```

So the area of the region enclosed by the lines x=0, x=6, y=2, and y=6 is 24 square units.