Propagation error in finding the perimeter and area, .

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SUMMARY

The discussion focuses on calculating the perimeter and area of a backyard with given dimensions and measurement errors. The length is 8.6 m and the width is 7 m, both with an accuracy of 0.05 m. The calculated perimeter is 31.4 m, but the user struggles to determine the error in this calculation. The correct method involves using the formula for error propagation, specifically the square root of the sum of the squares of the individual measurement errors.

PREREQUISITES
  • Understanding of basic geometry concepts, specifically perimeter and area calculations.
  • Familiarity with error propagation principles in measurements.
  • Knowledge of using the square root and squaring numbers for calculations.
  • Ability to apply measurement accuracy in practical scenarios.
NEXT STEPS
  • Learn about error propagation techniques in measurements.
  • Study the formulas for calculating perimeter and area of various geometric shapes.
  • Explore practical applications of measurement accuracy in real-world scenarios.
  • Investigate how to apply statistical methods to assess measurement errors.
USEFUL FOR

Students in mathematics or physics, educators teaching measurement concepts, and anyone interested in understanding error analysis in practical applications.

megkirch
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Homework Statement


I want to measure the size of my back yard. I estimate that I can measure the length and width of the yard using a tape measure to an accuracy of 0.05m. I find that the length of the yard is 8.6 m and the width is 7 m.



Calculate the perimeter of the yard and its error
Now calculate the area of the yard and its error


Homework Equations


s=square root(changeA)^2+(changeB)^2)


The Attempt at a Solution


I calculated the perimeter and got 31.4m. i can't figure out how to get the error in the perimeter. I thought it would be 8.55(2)+6.95(2) =31.0 -31.4=.4 but its not correct
 
Physics news on Phys.org
You say your accuracy is 0.05m.

Then the length is 8.60 m. the error in measurement is 0.05m
The width is 7.00m with a measurement error of 0.05m
 

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