Mia is building a three-sided shelter for her action figures. The shelter will
resemble a rectangle with one of the long sides removed. She has boards that
measure 36 inches, 39 inches, and 42 inches in length; all the boards are the
same width. Mia will need to convert some of these measurements into other
imperial units to build the shelter the way she wants. Answer the following
questions. Show your work. Record your answers below.
Question 1
Mia will use one of these boards for the length of the shelter. She knows she wants
the length of the shelter to measure 3.25 feet. She will use a different board for the
width of the shelter. The width of the shelter will be shorter than the length.
To convert 3.25 feet to inches, we multiply by 12 (since there are 12 inches in 1 foot):
3.25 feet * 12 inches/foot = 39 inches
So Mia will need to use the board that measures 39 inches for the length of the shelter.
What is the width of the shelter, measured in feet?
Since the width of the shelter will be shorter than the length, it could be one of the two remaining boards: 36 inches or 42 inches.
To convert inches to feet, we divide by 12 (since there are 12 inches in 1 foot):
36 inches / 12 inches/foot = 3 feet
42 inches / 12 inches/foot = 3.5 feet
So the width of the shelter could be either 3 feet or 3.5 feet.
Mia needs to cut the third board to match the width of the shelter. How many feet of
board will she need to cut off the existing board to reach this goal?
If the width of the shelter is 3 feet, then Mia will need to cut off the excess length of the third board. The third board is 42 inches long, which is equivalent to 3.5 feet.
To find out how much of the board she needs to cut off, we subtract the desired width (3 feet) from the existing length of the board (3.5 feet):
3.5 feet - 3 feet = 0.5 feet
Therefore, Mia will need to cut off 0.5 feet of the existing board to match the width of the shelter.
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 which board will cover all the space needed for the roof, we need to calculate the area of each board and compare it to the area of the shelter.
The area of a rectangle can be found by multiplying its length by its width.
1 square yard = 3 feet * 3 feet = 9 square feet
3 feet * 3 feet = 9 square feet
36 inches * 36 inches = 1296 square inches
To convert 1296 square inches to square feet, we divide by 144 (since there are 144 square inches in 1 square foot):
1296 square inches / 144 square inches/square foot = 9 square feet
From the calculations, we can see that all three boards have the same area of 9 square feet. Therefore, any of the three boards will cover all the space needed for the roof of the shelter.