Question 2

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?
Explain your answer, drawing a picture if necessary.
1 foot = 1/3 of a yard

Answer 1

To determine which board (if any) will cover the space needed for the roof, we first need to find out the area of each board in square yards.

1. First Board:

   • Area = 1 square yard (given).

2. Second Board:

   • Dimensions = 3 feet by 3 feet.
   • To convert feet into yards:
     • 1 foot = 1/3 yard.
     • Therefore, 3 feet = 3 * (1/3) yard = 1 yard.
   • Area = 1 yard * 1 yard = 1 square yard.

3. Third Board:

   • Dimensions = 36 inches by 36 inches.
   • To convert inches into yards:
     • There are 36 inches in a yard, so 36 inches = 36/36 yards = 1 yard.
   • Area = 1 yard * 1 yard = 1 square yard.

Now we can summarize the areas of all the boards:

• First Board: 1 square yard
• Second Board: 1 square yard
• Third Board: 1 square yard

Since all three boards have an area of 1 square yard, they each cover the same area of the roof, which is 1 square yard.

If the total area required for the roof is at most 1 square yard, then any of the boards in question will cover the space needed for the roof. However, if the area required for the roof exceeds 1 square yard, then none of the boards will be sufficient to cover it.

If you have a specific area requirement for the roof, please provide it so that we can determine if any of the boards are adequate.