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Am supposed to be (19.5+0)/2=9.75 then why Am=8.625 here

It seems like you're calculating an area, denoted by \( A_m \), and comparing it with a method where you average two areas, \( A_8 \) and \( A_9 \), as \(\frac{A_8 + A_9}{2}\).

From your explanation:

- \( A_8 = 19.50 \, \text{m}^2 \)
- \( A_9 = 0 \, \text{m}^2 \)
- You're expecting \( A_m \) to be the average of these two:  
\[
A_m = \frac{19.50 + 0}{2} = 9.75 \, \text{m}^2
\]

However, the given formula calculates \( A_m(8,9) \) as:
\[
A_m(8,9) = B_d m + S_d m = 10 \times 0.75 + 2 \times 0.75^2 = 8.625 \, \text{m}^2
\]

**Explanation of the Discrepancy:**

- The calculation you're referring to uses a specific method (likely related to trapezoidal or similar integration) to determine the area between two points (or sections). 
- \( A_m(8,9) \) doesn't seem to be a direct average of \( A_8 \) and \( A_9 \). Instead, it's likely calculated using a different approach, perhaps based on the geometry of the section between points 8 and 9.
- \( A_m(8,9) \) is computed directly using dimensions (like \( B_d m \) and \( S_d m \)), which may represent a different physical characteristic or formula than the simple average.

Would you like more details about the exact nature of these calculations? It would be useful to confirm the formula and context (e.g., structural engineering or another discipline).

### 5 Related Questions:
1. What do the terms \( B_d m \) and \( S_d m \) represent in this formula?
2. Is there a reason why \( A_m \) is not simply an average of \( A_8 \) and \( A_9 \)?
3. Could this calculation be related to a specific geometric shape (trapezoidal or other) between two sections?
4. Are you solving for areas in a structural analysis or civil engineering problem?
5. What are the exact units and definitions of the dimensions used in \( B_d \) and \( S_d \)?

### Tip:
Always verify if different formulas are used for calculating areas between two points to avoid confusion with averaging methods.

Understand why Am is calculated as 8.625 m² instead of the expected 9.75 m² when averaging two areas. This explanation delves into the formulas used for calculating Am(8,9) using geometric dimensions, likely in a structural or engineering context.

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