A model of a triangular lawn is scaled to have 1 cm represent 10 yards.



What is the area of the actual lawn?

The area of the actual triangular lawn can be determined by using the relationship between the scale model and the real object. To solve this, we need the area of the lawn model in the scale diagram and the scale factor provided, which is 1 cm = 10 yards.

### Let's walk through the general process:

1. **Determine the area of the model lawn (in cm²)**: 
   - If you know the dimensions of the lawn model, calculate the area using the formula for the area of a triangle:
   
   \[
   \text{Area of the triangle} = \frac{1}{2} \times \text{base} \times \text{height}
   \]

2. **Find the scale factor for the area**: 
   - The scale factor between linear measurements is 1 cm = 10 yards. This means every 1 cm on the model corresponds to 10 yards in real life.
   - The area scale factor is the square of the linear scale factor:
   
   \[
   \text{Area scale factor} = (10)^2 = 100
   \]
   
3. **Calculate the area of the actual lawn**: 
   - Multiply the area of the model by the area scale factor (100) to get the area of the actual lawn in square yards.

If you provide the dimensions or area of the triangular model, I can proceed with a specific calculation for the actual lawn's area.

Would you like to proceed with any specific measurements, or is there another step I can clarify?

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**Related questions:**
1. How do you find the area of a triangle when only given side lengths?
2. What if the scale was 1 cm = 5 yards? How would the area change?
3. How do you convert from square yards to square feet?
4. How would you calculate the perimeter of the actual lawn if the model perimeter is known?
5. How does the shape of a triangle affect its area formula?

**Tip**: Always remember that when scaling an object, linear dimensions are scaled by the factor \( k \), but areas are scaled by \( k^2 \).

A model of a triangular lawn is scaled to have 1 cm represent 10 yards. What is the area of the actual lawn?

Learn how to calculate the area of an actual triangular lawn based on a scaled model where 1 cm represents 10 yards. This problem involves geometric concepts such as the area of a triangle and scale factor conversions, making it ideal for students in Grades 7-10.

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