Calculating a soil area as a polygon

EDIT: 

@Fred_Kohlhepp 

It looks to me that you are assuming that the "b" points have the same y-coordinates as the corresponding "a" points. As far as I see that's not always the case and depends on the ground surface geometry.

Here is my suggestion (also working in P4E), following your way of using integration (my initial approach in the other thread was using polygon formulas)

The usage of the factor 0.99 was necessary because your Express "linterp" replacement fails when we use the endpoint 100ft.

The differences between your calculation and mine is not highly significant but noticeable. It also depends on the ground surface geometry.

The one chosen in the sheet is constant from x=9ft upwards, so differences only occur for the first two polygons:

By the way, I think that your approach with the integration is more suitable and targeted here than my way (other thread) with the polygon formulas.

Prime 4 sheet attached

@Werner_E @Fred_Kohlhepp ... Thank you all for trying to help, I really appreciate it. I did not go through the solutions in more details, but thought to provide this explanation to address @Werner_E 's questions...
I initially aimed to keep my question as simple and focused as possible, limiting it to a specific math-related point to avoid unnecessary complexity 😁, especially given the space constraints. However, it seems I need to provide more background and context to clarify what I’m trying to achieve.

I’m working on calculating soil pressure using what is called: "Trial Wedge Method", which is a graphical, visual, and iterative technique for determining the maximum active earth pressure acting on a wall. The method involves:

• Assuming a range of potential failure wedges,

• Calculating the soil weight and surcharge (though surcharge is beyond the scope of this question) for each wedge,

• Finding the center of gravity (CG) of each load (focusing on the soil only for now),

• Determining the combined CG and total load (This is also the next step beyond the scope of my question),

• And identifying the wedge that produces the maximum force on the wall.

A few screenshots are attached to illustrate the approach in general.

In Mathcad, my general process is as follows:

1. The maximum angle I’m evaluating is 54 degrees.

2. I want to divide this angle into a large number of finite increments (e.g., 1000 iterations), each representing a possible wedge. For each wedge, I calculate the soil area, convert it to weight, and determine its CG. (which I am trying to achieve), and save in the back scene

3. I’ll apply a similar process to the surcharge separately, (though that’s not the focus for now).

4. I then compute the combined CG of soil and surcharge and use it to determine the resulting force on the wall. (not the focus now)

5. Finally, I identify the wedge angle corresponding to the maximum combined loading.

The main challenge I’m facing is implementing this iterative process for the soil portion in Mathcad, specifically, automating the calculation of area, CG, and force for each wedge angle in the sequence. The concept is clear from the previously provided solution, but I’m unsure how to efficiently apply it across all iterations in the intended purpose that I am now explaining.

The second challenge is scalability. While my previously provided sample uses three stacked blocks, I need the equations to work for any number of courses (which I define as "NUM", typically ranging from 2 to 😎 without significantly increasing complexity.
I hope this answers some of the questions and gives a clearer picture of what I’m trying to do.
I will look into the provided solutions, in the sometime, I hope this explanation will give you both more insight into the end product that I need to achieve... Thanks again