Question

For the roof of the shelter, Mia has a board that measures 1 square yard, a second board that measures 3 feet by 3 feet, and a third board that measures 36 inches by 36 inches. Which of these, if any, will cover all the space needed for the roof?

Answer 1

To compare the area covered by each board, we need to convert all measurements to a consistent unit.

1 square yard is equal to 9 square feet.

The second board measures 3 feet by 3 feet, so its area is 3 feet * 3 feet = 9 square feet. This is equal to 1 square yard, so it will cover all the space needed for the roof.

The third board measures 36 inches by 36 inches, so its area is 36 inches * 36 inches = 1296 square inches. To convert this to square feet, we divide by 144 (since 12 inches = 1 foot, so 12 * 12 = 144 square inches in a square foot). Therefore, the area of the third board is 1296 square inches / 144 = 9 square feet. This is also equal to 1 square yard, so it will cover all the space needed for the roof.

In conclusion, both the second and third boards will cover all the space needed for the roof.