To determine which board will cover the roof of the shelter, we first need to calculate the area of each board in square feet.
Step 1: Identify the dimensions of the roof.
Since the shelter has a length of 39 inches and a width of 36 inches (or 3 feet), we convert these dimensions into feet:
- Length: \(39 , \text{inches} = \frac{39}{12} , \text{feet} = 3.25 , \text{feet}\)
- Width: \(36 , \text{inches} = \frac{36}{12} , \text{feet} = 3 , \text{feet}\)
Next, we can calculate the area of the roof:
\[
\text{Area of the roof} = \text{Length} \times \text{Width} = 3.25 , \text{feet} \times 3 , \text{feet} = 9.75 , \text{square feet}
\]
Step 2: Calculate the area of each board.
-
Board that measures 1 square yard:
Since 1 square yard is equal to \(3 , \text{feet} \times 3 , \text{feet} = 9 , \text{square feet}\).
-
Board that measures 3 feet by 3 feet:
\[
\text{Area} = 3 , \text{feet} \times 3 , \text{feet} = 9 , \text{square feet}
\]
-
Board that measures 36 inches by 36 inches:
Converting to feet:
\[
\text{36 inches} = \frac{36}{12} = 3 , \text{feet}
\]
\[
\text{Area} = 3 , \text{feet} \times 3 , \text{feet} = 9 , \text{square feet}
\]
Step 3: Compare the areas of the boards with the area of the roof.
- The area of the roof is 9.75 square feet.
- All three boards (1 square yard, 3 feet by 3 feet, and 36 inches by 36 inches) have an area of 9 square feet.
Since none of the boards can cover an area of 9.75 square feet, they are all insufficient to cover the entire roof space.
Conclusion:
None of the boards will cover the roof space needed for the shelter, as they all measure 9 square feet, which is less than the required 9.75 square feet.
