Question

1. the tub in paige’s bathroom covers the tile floor as shown below. how many square tiles are on the floor, including the tiles under the tub?

Explanation:

Step1: Determine the dimensions of the tub's area (rectangle)

Looking at the grid, the tub (rectangle) spans 7 units in length (horizontal) and 4 units in height (vertical). The area of a rectangle is calculated by the formula $A = l \times w$, where $l$ is length and $w$ is width. So, the area of the tub's rectangular base is $7 \times 4 = 28$ square tiles. Wait, but actually, the total floor (including under tub) – wait, no, the problem is "How many square tiles are on the floor, including the tiles under the tub?" Wait, maybe the total floor is a larger rectangle? Wait, looking at the grid, the total floor (the big rectangle) has length 9 (horizontal) and height 8 (vertical)? Wait, no, let's re - examine. Wait, the tub is a rectangle, but the total floor: from the grid, the horizontal tiles: let's count the columns. The tub is in a rectangle, and the total floor (the big rectangle) has 9 columns (horizontal) and 8 rows (vertical)? Wait, no, maybe I misread. Wait, the tub's rectangle: looking at the grid, the tub's rectangle has length 7 (number of squares along the top: from left to right, 7 squares) and height 4 (from top to bottom, 4 squares). But the total floor (including under tub) – wait, the big rectangle (the entire floor) has length 9 (horizontal: 9 squares) and height 8 (vertical: 8 squares)? Wait, no, let's count the grid. The lower part (below the tub) has 4 rows (vertical) and 9 columns (horizontal). The tub's part has 4 rows (vertical) and 7 columns (horizontal). Wait, no, the total number of tiles: the total floor is a rectangle with length 9 and height 8? Wait, no, let's count the vertical and horizontal. Let's see, the vertical direction: from top to bottom, the tub is in the first 4 rows, and below it, there are 4 rows, so total 8 rows. Horizontal direction: 9 columns. Wait, but the tub is a rectangle with length 7 and height 4. But the problem is "including the tiles under the tub", so we need to find the area of the entire floor (the big rectangle). Wait, maybe the total floor is a rectangle with length 9 and width 8? Wait, no, let's count the number of tiles. Let's count the horizontal tiles: the big rectangle (total floor) has 9 tiles in a row (horizontal) and 8 tiles in a column (vertical). So the area is $9\times8 = 72$? Wait, no, that can't be. Wait, maybe the tub is a rectangle with length 7 and height 4, and the total floor is the area of the big rectangle. Wait, maybe I made a mistake. Wait, let's look at the grid again. The tub is a rectangle with length 7 (horizontal: 7 squares) and height 4 (vertical: 4 squares). But the total floor (including under tub) – the big rectangle: horizontal squares: 9, vertical squares: 8. So area is $9\times8=72$? Wait, no, maybe the tub is part of it, but the question is "including the tiles under the tub", so we need to calculate the area of the entire floor (the big rectangle). Let's confirm:

Horizontal (length): count the number of squares along the bottom row (the lower part of the floor) – there are 9 squares.

Vertical (height): count the number of rows – from top to bottom, there are 8 rows (4 rows for the tub's area and 4 rows below).

So the area of a rectangle is $A = length\times height$. So $A=9\times8 = 72$? Wait, no, wait, the tub is a rectangle with length 7 and height 4, but the total floor is the big rectangle. Wait, maybe the tub is in a rectangle of 7x4, but the total floor is 9x8? Wait, let's count the tiles:

Each small square is a tile. Let's count the number of tiles in the horizontal direction (columns): 9.

Number of tiles in the vertical direction (rows): 8.

So total number of tiles is $9\times8=72$? Wait, no, maybe I messed up. Wait, the tub is a rectangle with length 7 and height 4, but the total floor (including under tub) is the area of the big rectangle. Wait, maybe the correct dimensions are: length = 9, height = 8. So area is $9\times8 = 72$? Wait, no, let's check again. Wait, the vertical rows: the tub is in the first 4 rows (from top), and below it, there are 4 rows, so total 8 rows. Horizontal columns: 9 columns. So $9\times8 = 72$. But wait, maybe the tub is a rectangle with length 7 and height 4, but the total floor is the big rectangle. Wait, maybe I made a mistake in the tub's area. Wait, the problem is "including the tiles under the tub", so we need to find the area of the entire floor (the big rectangle). So if the big rectangle has length 9 and height 8, then area is $9\times8=72$. Wait, but let's count the tiles:

Row 1 (top row): 9 tiles

Row 2: 9 tiles

Row 3: 9 tiles

Row 4: 9 tiles (tub is here, but we include under tub)

Row 5: 9 tiles

Row 6: 9 tiles

Row 7: 9 tiles

Row 8: 9 tiles

Total tiles: $9\times8 = 72$. Wait, but maybe the tub is a rectangle with length 7 and height 4, but the total floor is the big rectangle. So the answer is 72? Wait, no, maybe I misread the grid. Wait, the tub is a rectangle with length 7 and height 4, but the total floor is length 9 and height 8. So $9\times8 = 72$.

Wait, another way: the tub's rectangle: length 7, height 4. The area under the tub (but we need including, so total floor). Wait, maybe the total floor is a rectangle with length 9 and height 8. So $A = 9\times8=72$.

Step2: Confirm the calculation

The formula for the area of a rectangle is $A=l\times w$. Here, $l = 9$ (number of horizontal tiles) and $w = 8$ (number of vertical tiles). So $A=9\times8 = 72$.

Answer:

72