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? Explain your answer, drawing a picture if necessary. 1 foot = 1/3 of a yard
To determine if any of the boards will cover all the space needed for the roof, we need to compare the measurements of each board to the total area needed.
First, let's convert the measurements of each board to the same unit.
1 square yard is equal to 3 feet * 3 feet = 9 square feet.
1 yard is equal to 3 feet, so 1/3 of a yard is equal to 1 foot.
36 inches is equal to 36 inches / 3 = 12 feet.
Based on the conversions, each board has the following measurements:
- 1 square yard board: 9 square feet
- 3 feet by 3 feet board: 9 square feet
- 36 inches by 36 inches board: 12 feet by 12 feet = 144 square feet
Since all three boards have the same area of 9 square feet, we can conclude that any of the three boards will cover all the space needed for the roof.