You are surveying a plot of land with uneven terrain. You have previously measured your average pace length to be 0.75 meters on flat ground. However, on this terrain, you estimate that your average pace length is reduced by 10%. Your number of paces are as follows: 305, 302.5, 306, 310. Calculate the distance. 

To calculate the distance considering the reduced pace length on uneven terrain, follow these steps:

### 1. Adjust the Average Pace Length
Since your average pace length on flat ground is 0.75 meters and you estimate a 10% reduction on uneven terrain:

\[
\text{Reduced Pace Length} = 0.75 \times (1 - 0.10) = 0.75 \times 0.90 = 0.675 \text{ meters}
\]

### 2. Calculate the Average Number of Paces
Find the average of the given number of paces:

\[
\text{Average Paces} = \frac{305 + 302.5 + 306 + 310}{4} 
\]

\[
\text{Average Paces} = \frac{1223.5}{4} = 305.875 \text{ paces}
\]

### 3. Calculate the Distance
Multiply the average number of paces by the reduced pace length:

\[
\text{Distance} = 305.875 \times 0.675 \text{ meters}
\]

\[
\text{Distance} = 206.468125 \text{ meters}
\]

**The estimated distance of the survey line on the uneven terrain is approximately 206.47 meters.**

Would you like more details or have any questions?

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Here are 5 related questions you might find interesting:

1. How can you accurately determine the reduction in pace length due to terrain?
2. What methods can you use to verify the accuracy of your distance estimation on uneven ground?
3. How does the slope of the terrain impact the accuracy of pacing measurements?
4. What are the limitations of using pacing as a measurement technique in professional surveys?
5. How can technology (like GPS) be used to complement pacing in difficult terrains?

**Tip:** When surveying uneven terrain, consider taking multiple measurements to account for variations in your stride length.

Learn how to calculate distance on uneven terrain by adjusting pace length. This problem involves applying arithmetic and measurement concepts to estimate distance accurately. Suitable for students in Grades 7-9.

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