Question

1 vanessa wants to cover her closet floor with tiles that are \\(\frac{1}{3}\\) foot on each side. the closet is \\(3\frac{1}{3}\\) feet wide and 6 feet deep.
a. how many tiles will vanessa need to cover the closet floor? use the picture to help you.
\\(\underline{186}\\) tiles
b. how many of vanessa’s tiles would it take to cover 1 square foot?
\\(\underline{9}\\) tiles
c. use your answers to parts a and b to find the area of the closet floor in square feet.
\\(\underline{20}\\) square feet
\\(\underline{10 \times 18 = 180}\\)
(number sentence)

Explanation:

Part a

Step1: Find area of closet floor

The closet is a rectangle, so area \( A = \text{width} \times \text{depth} \). Width is \( 3\frac{1}{3}=\frac{10}{3} \) feet, depth is \( 6 \) feet. So \( A=\frac{10}{3} \times 6 = 20 \) square feet.

Step2: Find area of one tile

Tile is a square with side \( \frac{1}{3} \) foot, so area \( a = (\frac{1}{3})^2=\frac{1}{9} \) square feet.

Step3: Find number of tiles

Number of tiles \( n=\frac{\text{Area of closet}}{\text{Area of one tile}}=\frac{20}{\frac{1}{9}} = 20\times9 = 180 \).

Step1: Area of one tile

As above, tile area \( a = (\frac{1}{3})^2=\frac{1}{9} \) square feet.

Step2: Tiles per square foot

To find tiles per 1 square foot, calculate \( \frac{1}{\text{Area of one tile}}=\frac{1}{\frac{1}{9}} = 9 \).

Step1: Use part a and b

From part a, total tiles = 180; from part b, tiles per square foot = 9.

Step2: Calculate area

Area \( = \frac{\text{Total tiles}}{\text{Tiles per square foot}}=\frac{180}{9}=20 \) square feet.

Answer:

180

Part b