The carpet you like costs $30 per square yard, installed. The area of the room is 334 square feet. In square yards, the area of the room is 37.11 square yards. The cost of carpeting the room is $1113.33.

Explain briefly what strategies you used to find the area of the room:

- The strategy was to find the area of a rectangle using base times height.
- Then, I found the area of a trapezoid using the formula: $(\text{base}_1 + \text{base}_2) / 2 \times \text{height}$.
- The total area was 334 square feet, which I converted to square yards (9 square feet = 1 square yard).
- Total area: $334 \, \text{ft}^2 \times \text{yard}^2 / 9 \, \text{ft}^2 = 37.11 \, \text{yd}^2$.
- The cost was calculated by multiplying $30 per square yard by the total area in square yards.

You would also like to purchase baseboard at $3.25 per linear foot. How much will it cost you for baseboard?

Explain briefly how finding the cost of the baseboard is different from finding the cost of the carpet:

- Finding the cost of the baseboard involves measuring the perimeter of the room, as baseboards are priced per linear foot.
- In contrast, the cost of the carpet is based on the area of the floor, priced per square yard.

To calculate the cost of re-carpeting the room, we follow these steps:

1. **Convert the Area from Square Feet to Square Yards:**
The area of the room is given as 334 square feet. Since carpet pricing is in square yards, we need to convert the area from square feet to square yards. There are 9 square feet in a square yard, so we divide the room area by 9.
[tex]\[ \text{Room Area in Square Yards} = \frac{334}{9} \approx 37.11 \text{ (rounded to two decimal places)} \][/tex]

2. **Calculate the Cost:**
The cost of carpet per square yard is $30. To find the total cost to carpet the room, we need to multiply the room area in square yards by this cost.
[tex]\[ \text{Total Carpet Cost} = 37.11 \times 30 = \$1113.30 \text{ (rounded to two decimal places)} \][/tex]
Therefore, the cost to re-carpet the room is approximately $1113.30.

For finding the cost of the baseboard, the strategy is different because baseboard is priced per linear foot, not per square foot or square yard. To calculate the cost for the baseboard, you would follow these steps:

1. **Find the Perimeter of the Room:**
The perimeter is the total length around the room. If we knew the length and width of the room, we could calculate the perimeter $P$ as:
[tex]\[ P = 2(\text{Length} + \text{Width}) \][/tex]
However, since the exact dimensions of the room are not provided in the question, we cannot calculate the perimeter.

2. **Calculate the Cost:**
Once you know the perimeter $P$ in feet, you would multiply it by the cost per linear foot of the baseboard which is $3.25.
[tex]\[ \text{Total Baseboard Cost} = P \times 3.25 \][/tex]
Without the perimeter, we cannot calculate the total cost of the baseboard.

In summary, for carpeting, we use the area of the room to calculate cost, and for baseboard, we use the perimeter of the room. The former requires square yard measurements while the latter requires linear foot measurements.