To determine which of the boards can cover the roof of the shelter, we first need to calculate the area of the roof.
The dimensions of the shelter are 39 inches by 36 inches.
Step 1: Calculate the area of the roof
Convert the dimensions of the roof from inches to square feet:
- 39 inches = 39/12 feet = 3.25 feet
- 36 inches = 36/12 feet = 3 feet
Now calculate the area in square feet: \[ \text{Area} = \text{length} \times \text{width} = 3.25 , \text{ft} \times 3 , \text{ft} = 9.75 , \text{square feet} \]
Step 2: Calculate the area of each board
-
First board (1 square yard): \[ 1 , \text{square yard} = 9 , \text{square feet} \]
-
Second board (3 feet by 3 feet): \[ \text{Area} = 3 , \text{ft} \times 3 , \text{ft} = 9 , \text{square feet} \]
-
Third board (36 inches by 36 inches): Convert from inches to feet first. \[ 36 , \text{inches} = 3 , \text{feet} \] Then calculate the area: \[ \text{Area} = 3 , \text{ft} \times 3 , \text{ft} = 9 , \text{square feet} \]
Step 3: Compare the areas
- The area of the roof needed is 9.75 square feet.
- The areas of the boards are as follows:
- First board: 9 square feet
- Second board: 9 square feet
- Third board: 9 square feet
None of the boards (1 square yard, 3 feet by 3 feet, or 36 inches by 36 inches) cover the total area of the roof of 9.75 square feet.
Conclusion
None of the boards will cover all the space needed for the roof, as each board has an area less than 9.75 square feet.
25 answers