Questions: Using Equation 2, calculate the areas of each triangle using the bases and heights you measured. The percent difference between the areas is calculated using the following formula. (Note the absolute value bars in the numerator.) percent difference = 2 × area 1 -area 2 / (area 1 +area 2) × 100 Calculate the percent difference. Because of limited precision of the measurements, if the areas are within 10% of each other, we can consider them about the same. Kepler's Laws Lab Worksheet This sheet is to show work and calculations related to particular questions. Your work should be correct and consistent with the answers you submit in Canvas. To show work, you don't have to recopy any formulas, but you DO need to show the formulas written with your numbers substituted in and your calculated answer. Include the proper units with all your answers. Work leading up to Question 2 Show your calculations for the triangle areas using Equation 2. (units are mm^2)

Using Equation 2, calculate the areas of each triangle using the bases and heights you measured. The percent difference between the areas is calculated using the following formula. (Note the absolute value bars in the numerator.) percent difference = 2 × area 1 -area 2 / (area 1 +area 2) × 100 Calculate the percent difference. Because of limited precision of the measurements, if the areas are within 10% of each other, we can consider them about the same. Kepler's Laws Lab Worksheet This sheet is to show work and calculations related to particular questions. Your work should be correct and consistent with the answers you submit in Canvas. To show work, you don't have to recopy any formulas, but you DO need to show the formulas written with your numbers substituted in and your calculated answer. Include the proper units with all your answers. Work leading up to Question 2 Show your calculations for the triangle areas using Equation 2. (units are mm^2)
Transcript text: Using Equation 2, calculate the areas of each triangle using the bases and heights you measured. The percent difference between the areas is calculated using the following formula. (Note the absolute value bars in the numerator.) \[ \text { percent difference }=2 \times \frac{\mid \text { area } 1 \text {-area } 2 \mid}{\text { area } 1 \text { +area } 2} \times 100 \] Calculate the percent difference. Because of limited precision of the measurements, if the areas are within $10 \%$ of each other, we can consider them about the same. Kepler's Laws Lab Worksheet This sheet is to show work and calculations related to particular questions. Your work should be correct and consistent with the answers you submit in Canvas. To show work, you don't have to recopy any formulas, but you DO need to show the formulas written with your numbers substituted in and your calculated answer. Include the proper units with all your answers. Work leading up to Question 2 Show your calculations for the triangle areas using Equation 2. (units are $\mathrm{mm}^{2}$ )
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Solution

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Solution Steps

To solve the given problem, we need to follow these steps:

  1. Calculate the areas of the triangles using the given bases and heights.
  2. Use the formula for percent difference to find the percent difference between the two areas.
  3. Determine if the areas are within 10% of each other.
Solution Approach
  1. Calculate the areas of the triangles: Use the formula for the area of a triangle, \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \).
  2. Calculate the percent difference: Use the given formula for percent difference.
  3. Compare the percent difference: Check if the percent difference is within 10%.
Step 1: Calculate the Areas of the Triangles

Using the formula for the area of a triangle, \( \text{Area} = \frac{1}{2} \times \text{base} \times \text{height} \):

For the first triangle: \[ \text{Area}_1 = \frac{1}{2} \times 10 \, \text{mm} \times 5 \, \text{mm} = 25 \, \text{mm}^2 \]

For the second triangle: \[ \text{Area}_2 = \frac{1}{2} \times 12 \, \text{mm} \times 6 \, \text{mm} = 36 \, \text{mm}^2 \]

Step 2: Calculate the Percent Difference

Using the formula for percent difference: \[ \text{percent difference} = 2 \times \frac{\left| \text{Area}_1 - \text{Area}_2 \right|}{\text{Area}_1 + \text{Area}_2} \times 100 \]

Substituting the values: \[ \text{percent difference} = 2 \times \frac{\left| 25 - 36 \right|}{25 + 36} \times 100 = 2 \times \frac{11}{61} \times 100 \approx 36.0656\% \]

Step 3: Determine if the Areas are Within 10% of Each Other

We compare the percent difference to 10%: \[ 36.0656\% > 10\% \]

Thus, the areas are not within 10% of each other.

Final Answer

\[ \boxed{\text{Percent Difference: } 36.0656\%} \] \[ \boxed{\text{Are the areas within 10% of each other? No}} \]

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