your school is putting on a prom fashion show, and you are in charge of building a platform to serve as a stage. Main stage is a rectangle and the runways is a square. the length of the main stage is three times the length of the runway and the width of the main stage is two times the length og the runway.

write a function A(x) for the area of the entire stage and draw the stage.

A(x)=x^2+6x^2

A(x)= 7x^2

To write the function A(x) for the area of the entire stage, where x represents the length of the runway, we can follow these steps:

1. First, let's determine the dimensions of the main stage in terms of the runway's length (x).
- The length of the main stage is three times the length of the runway, so it would be 3x.
- The width of the main stage is two times the length of the runway, so it would be 2x.

2. Next, we can calculate the area of the main stage by multiplying its length and width:
- The area of the main stage would be (3x) * (2x) = 6x^2.

3. The runway is a square, so its length and width are equal to x.
- The area of the runway would be x * x = x^2.

4. Finally, to calculate the area of the entire stage, we need to add the area of the main stage and the area of the runway:
- A(x) = area of the main stage + area of the runway
= 6x^2 + x^2
= 7x^2.

So, the function A(x) for the area of the entire stage is A(x) = 7x^2.

To draw the stage, we can visualize it as follows:

______________________
| |
| Main Stage |
| (3x * 2x) |
| |
| |
|______________________|

__________ __________
| | | |
| Runway | | Runway |
| (x * x) | | (x * x) |
|__________| |__________|

I hope this helps! Let me know if you have any further questions.