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 the boards, if any, will cover all the space needed for the roof? Explain your
answer,
The first board that measures 1 square yard is equivalent to an area of 1 yard by 1 yard, or 3 feet by 3 feet.
The second board that measures 3 feet by 3 feet is, as mentioned, equivalent to an area of 3 feet by 3 feet.
The third board that measures 36 inches by 36 inches is also equivalent to an area of 3 feet by 3 feet.
Therefore, all three boards are equivalent in size and will cover all the space needed for the roof.
1 foot = 1/3 of a yard
Apologies for the mistake. You are correct in stating that 1 foot is equivalent to 1/3 of a yard.
To revise the answer:
The first board that measures 1 square yard is equivalent to an area of 1 yard by 1 yard, which is equivalent to an area of 3 feet by 3 feet.
The second board that measures 3 feet by 3 feet is equivalent to an area of 1 yard by 1 yard.
The third board that measures 36 inches by 36 inches is equivalent to an area of 1 yard by 1 yard.
Therefore, all three boards are equivalent in size and will cover all the space needed for the roof.
To determine which board, if any, will cover all the space needed for the roof, we need to compare the measurements of the boards to the total area needed for the roof.
First, let's convert the measurements to a common unit. Since 1 yard is equal to 3 feet, the board that measures 1 square yard is equivalent to a board that measures 3 feet by 3 feet.
Now, we have two boards with the same dimensions: one measuring 3 feet by 3 feet and one measuring 36 inches by 36 inches. Since 1 foot is equal to 12 inches, we can see that both boards have the same area.
To calculate the area of each board, we use the formula: Area = Length x Width.
For the 3 feet by 3 feet board:
Area = 3 feet x 3 feet = 9 square feet
For the 36 inches by 36 inches board:
Area = 36 inches x 36 inches = 1296 square inches.
Since 1 square foot is equal to 144 square inches, we can convert the area of the 36 inches by 36 inches board:
Area = 1296 square inches ÷ 144 = 9 square feet.
Now that we know both boards have the same area of 9 square feet, either one of them can cover all the space needed for the roof.
Therefore, both the board that measures 1 square yard (3 feet by 3 feet) and the board that measures 36 inches by 36 inches will cover all the space needed for the roof.