Question

A room is being carpeted and the model of the carpet. If the cost is 1 ft.^2 of carpet is $30, what is the cost of the whole carpet?
Imagine a simple rocket ship sort of shape for the model of the carpet.
The top pointy part is labelled "1 ft", the left and right sides of the large rectangle are both labelled "4 ft", the bottom of the entire rectangular shape is labelled "5 ft", and the "wings" on the sidees of the rectangle are both labelled "2 ft". The entire model is labelled "8 ft" as a whole by a separate line on the side.

A. $610
B. $1,170
C. $1,515
D. $1,060

Answer 1

To calculate the cost of carpeting the entire room based on the given dimensions of the rocket ship-shaped model, we first need to find the area of that shape.

1. **Calculate the area of the rectangle:**
- The rectangle's width (height of the rocket) is 5 ft, and the width between the left and right sides is 4 ft.
\[
\text{Area of rectangle} = \text{width} \times \text{height} = 4 \, \text{ft} \times 5 \, \text{ft} = 20 \, \text{ft}^2
\]

2. **Calculate the area of the triangular part:**
- The triangle on top has a height of 1 ft and a base of 4 ft.
\[
\text{Area of triangle} = \frac{1}{2} \times \text{base} \times \text{height} = \frac{1}{2} \times 4 \, \text{ft} \times 1 \, \text{ft} = 2 \, \text{ft}^2
\]

3. **Now, we need to calculate the total area of the model:**
\[
\text{Total area} = \text{Area of rectangle} + \text{Area of triangle} = 20 \, \text{ft}^2 + 2 \, \text{ft}^2 = 22 \, \text{ft}^2
\]

4. **Calculate the cost of carpeting:**
- The cost per square foot is $30.
\[
\text{Total cost} = \text{Total area} \times \text{cost per square foot} = 22 \, \text{ft}^2 \times 30 \, \text{\$/ft}^2 = 660 \, \text{\$}
\]

Since the dimensions mentioned and interpretations do not match any option suggested (i.e., 660 is not among A, B, C, or D), please verify if the shape dimensions you provided have an additional area to be accounted for or if there are any other components leading to a higher area calculation. If further clarification does not reveal additional information, the answer based on the calculated area comes from the model description.

However, if we consider that the total cost must align with the available options, please provide any extra details or verify the model's area interpretation since the given options suggest higher costs (like options A, B, C, or D).