To determine which part of the carpet should be excluded so that the total cost is exactly $960, we should first calculate the area of the carpet that corresponds to that budget.
Given that the cost of carpet is $20 per square foot, we can find the total area we can afford with the budget of $960:
\[ \text{Total area} = \frac{\text{Total cost}}{\text{Cost per square foot}} = \frac{960}{20} = 48 \text{ square feet} \]
Next, we need to calculate the area of each part of the outlined carpet (the right triangle on the left, the rectangle, the isosceles triangle, and the right triangle on the right) to see how they add up.
Without the exact dimensions of the shapes provided in the image (which I don't have access to), I cannot calculate the exact areas of each component. However, the goal is to either identify the part you need to exclude based on the areas available or confirm if the total area of all parts exceeds 48 square feet.
- If the total area (sum of all parts) is more than 48 square feet, identify which part has the largest area to exclude it.
- If you can sum the areas of the parts, you can determine their individual contributions to find which part to exclude.
To conclude, based on your calculations:
- If the combined area of all four components exceeds 48 square feet, exclude the part with the largest area.
- If specific areas are known and total 48 square feet without exclusion, then no part needs to be excluded.
Please specify the dimensions of the carpet sections if you would like a more precise calculation!