Question

Paulina is remodeling her bathroom. The tile she has chosen is shown below. There are squares and trapezoids in the tile. The side length of each square in the tile is x centimeters. The height and the length of one of the bases of each trapezoid is x centimeters. The other length is 2x centimeters.

Part A
Write a simplified equation to solve for x in terms of AT, the area of the tile. If necessary, use rational coefficients instead of root symbols.

Part B
If the tile is a square with a length of b centimeters, what would AT be in terms of b?

Part C
Using the equation from part B, rewrite the equation for x in terms of b and explain how you simplify it. What does this equation really represent?

Part D
Using the equation from part C, solve for x if the side length of the tile is 6 centimeters.

Part E
After seeing her remodeled bathroom, Paulina’s friend Sabrina also wants to remodel her bathroom. The tile she has chosen is shown below.

a square tile in a blue and white checkerboard pattern with four small squares per side

If all of the smaller squares have sides c centimeters long, write an expression for the area of the whole tile, AT, and find the area of the tile if the length of the small squares is 2.5 centimeters.

Part F
Once she completes a wall, Sabrina notices that the number of squares along each side of the wall is equal to the number of square centimeters in each tile’s area. Write and solve an equation for the number of squares on the wall, SW.

Part G
Write an equation for the area of the wall, AW. Then, solve for the area of the wall.

Answer 1

?

Answer 2

i literally have no idea i cant even read any of the questions tbh bc i had ADD

Answer 3

*have

Answer 4

ok

Answer 5

give me a sec

Answer 6

im sorry :(

Answer 7

Your fine

Answer 8

ok so find the formula for the trapezoid

Answer 9

jsjdj idontknowhowlol

Answer 10

ok step by step

Answer 11

huh

Answer 12

So part A wants you to find a simplified equation

Answer 13

The equation for a trapezoid is
A=
a+b/2h

Answer 14

ok

Answer 15

ok but what next (im so sorry im rlly dumb)

Answer 16

No, your not dumb, you don't understand.

Answer 17

Yeah we all don't understand something sometimes

Answer 18

thanks for the reassurance that was very nice of u guys. :) so what do i do next?

Answer 19

Solve for x and no prob

Answer 20

ok we know 2x is one side

Answer 21

ok

Answer 22

\(\color{#0cbb34}{\text{Originally Posted by}}\) @leila123456
ok we know 2x is one side
\(\color{#0cbb34}{\text{End of Quote}}\)
This is correct, but there is more to it than 2x.

Answer 23

ok

Answer 24

Is there an image for the homework?

Answer 25

yes ill send it

Answer 26

ok

Answer 27

theres this one if this is what u meant

Answer 28

Very helpful, thanks.

Answer 29

yeah

Answer 30

Don't look at it wrong, it looks like a box at a certain angle.

Answer 31

yep they try to trick you by doing that

Answer 32

Is there anything else, like numbers?

Answer 33

no

Answer 34

ok then

Answer 35

But how will you know it has to rotate(sorry just need a clarification)

Answer 36

@finnwolfhard, Can you provide a picture. It does say shown below.

Answer 37

\(\color{#0cbb34}{\text{Originally Posted by}}\) @finnwolfhard
theres this one if this is what u meant
\(\color{#0cbb34}{\text{End of Quote}}\)
There is a picture.

Answer 38

Write a simplified equation to solve for x in terms of \(\sf A_T\), the area of the tile

Now, the tile has four little squares in the center and then trapezoids around it.
But it's one large square by itself.

The formula for the area of a square is
Area = side * side
or
area = side^2

Answer 39

The little squares in the center each have a side length of 'x'
The trapezoid has two bases. One side of the base is adjacent to the smaller square so it's length is also x.
However the other base that makes up the edge of the larger square (which is the whole tile) has a length of 2x

and so we have 2 such trapezoid bases with a base of 2x
So what's the total length of one side of our tile?

Answer 40

Try not to get confused by all the colors in the diagram

Answer 41

Here, I took the liberty and went out of my way to color it in for you. We want to find the length of the blue line

We have 2x which is half of that so just double it and you'd have found the length of one side of our tile

And then remember the formula for area

\(\sf A_T = (side)^2\)

Answer 42

Then for part b, the area formula for a square is what I gave you above.

If the side length is B, then just replace 'side' with 'B'

Then for part c
You set what you got in part A equal to what you're getting in part B

But back to part A, what is the length of the side of the tile in terms of x?