First, we need to determine the area required for the roof of the shelter. Since the roof will be covering the area of the shelter, which has a length of 39 inches and a width of 36 inches, we will calculate that area in square inches and then convert it to square feet.
-
Calculate the area of the roof in square inches:
\[
\text{Area} = \text{Length} \times \text{Width} = 39 \text{ inches} \times 36 \text{ inches} = 1404 \text{ square inches}
\]
-
Convert the area to square feet (since there are 144 square inches in a square foot):
\[
\text{Area in square feet} = \frac{1404 \text{ square inches}}{144 \text{ square inches/square foot}} \approx 9.75 \text{ square feet}
\]
Now we need to evaluate the areas of the available boards:
Board 1: 1 square yard
- One square yard is equal to:
\[
1 \text{ square yard} = 3 \text{ feet} \times 3 \text{ feet} = 9 \text{ square feet}
\]
Board 2: 3 feet by 3 feet
- The area is:
\[
\text{Area} = 3 \text{ feet} \times 3 \text{ feet} = 9 \text{ square feet}
\]
Board 3: 36 inches by 36 inches
- First, convert the measurements to feet:
\[
36 \text{ inches} = 3 \text{ feet}
\]
- Then calculate the area:
\[
\text{Area} = 3 \text{ feet} \times 3 \text{ feet} = 9 \text{ square feet}
\]
Comparison of Available Boards
- Board 1 (1 square yard): 9 square feet
- Board 2 (3 feet by 3 feet): 9 square feet
- Board 3 (36 inches by 36 inches): 9 square feet
Conclusion
All three boards (the 1 square yard board, the 3 feet by 3 feet board, and the 36 inches by 36 inches board) precisely measure 9 square feet each, which is sufficient to cover the required roof area of approximately 9.75 square feet.
Therefore, none of the boards will cover the entire roof since they all measure 9 square feet, which is slightly less than the required area of 9.75 square feet. Mia will need to find additional material or combinations to cover the full area of the roof.
