Question

Help?

Answer 1

Any thoughts to how you would approach this?

Answer 2

Well I thought it was \[A=\frac{ d^2 }{ 2 }\] but I don't think that is even close to right.

Answer 3

The area of an object is it's width (base) multiplied by it's height.

Answer 4

For squares it's just side multiplied by side (since all lengths for it's sides are the same value).

Answer 5

I'll give you a hint. Pythagoras

Answer 6

Pythagorean/Pythagoras theorem?Huh?

Answer 7

Pythagoras is the guy who found the theorem, lol

Answer 8

But yes, you would say Pythagorean Theorem.

Answer 9

Do you see how it could be applied here?

Answer 10

no?

Answer 11

The diagonal from the center of the square to the corner is how long?

Answer 12

6yd

Answer 13

How long is it from corner to corner?

Answer 14

12 yd

Answer 15

What shape does that diagonal create?

Answer 16

oh I see now... a triangle

Answer 17

You got it? (:

Answer 18

maybeeeeeeeeee

Answer 19

Well what are you thinking you should do next

Answer 20

Well you mentioned the pythagorean theorem so do you write it out that way????

Answer 21

Do you know how to use pythagorean's theorem?

Answer 22

\[a^2+b^2=c^2\]

Answer 23

then the 12 you be placed into c right?

Answer 24

Yes, c is the hypotenuse.

Answer 25

So then \[a^2+b^2=12^2\]?

Answer 26

Correct.

a and b are the sides of the triangle. But since this is a square, what can we do with our formula?

Answer 27

I'm not sure, I've only done the pythagorean theorem with a single missing variable and never like this.

Answer 28

You have to think about this one.

Answer 29

About the sides of this 'triangle' that are actually sides of what shape?

Answer 30

The square?

Answer 31

Yes

Answer 32

And sides of a square are?

Answer 33

Not sure on that part?

Answer 34

They're equal.

Answer 35

Oh I thought you were asking what the length would be I was like ummm...

Answer 36

lol

Answer 37

That makes a 100% more sense LOL

Answer 38

Haha, so what do you think the next step is?

Answer 39

Not sure what you would do without having at least one of the variables

Answer 40

But if the sides are the same length, what can you dew?

Answer 41

not sure?

Answer 42

If two sticks are the same length, I can represent them with the same variable.

Answer 43

so instead of a and b you could just use say a?

Answer 44

Yes

Answer 45

okay

Answer 46

So what would I have to do next?

Answer 47

\[a^2 + a^2 = 12^2\]

Answer 48

What could you do on the left side

Answer 49

All I can think of is combine like variables but that doesnt sound right

Answer 50

what is a + a

Answer 51

a? I'm so confused??

Answer 52

a + a = 2a

Answer 53

so 2a then wouldnt you have to add the exponent?

Answer 54

or no?

Answer 55

yes

Answer 56

I was just illustrating the concept of adding variables.

Answer 57

oh okie

Answer 58

So would it just be \[2a^2\]? bc a^2 + a^2 is 2a^2

Answer 59

yes

Answer 60

So \[2a^2=12^2\] then what?

Answer 61

Solve for a, which is the side of a square.

Answer 62

So you get \[a^2=6^2\]?

Answer 63

PEMDAS

Exponents > Multiplication

Answer 64

So I do what???

Answer 65

Don't divide by 2, do the exponent on 12 first

Answer 66

12^2 = ?

Answer 67

Sorry I was doing the math so it would be 144 then divide that by the 2 to get \[a^2=72\]?

Answer 68

Is that right?

Answer 69

yes

Answer 70

Keep going

Answer 71

So then plug it in as \[2*72=12^2\]????

Answer 72

what

Answer 73

I mean 2 times 72 is 12^2 but what are you trying to do

Answer 74

Idunno I'm lost

Answer 75

\(\color{#0cbb34}{\text{Originally Posted by}}\) @lexxii
Sorry I was doing the math so it would be 144 then divide that by the 2 to get \[a^2=72\]?
\(\color{#0cbb34}{\text{End of Quote}}\)

Answer 76

Lets go back to here. What do you do next?

Answer 77

Then wouldnt you plug that in? I'm confused.

Answer 78

We need to solve for a.

Answer 79

But a is not isolated. We have an exponent there. How do we get rid of it?

Answer 80

\[\sqrt{a}\]??

Answer 81

\[\sqrt (a^2) = a \]

Correct

Answer 82

And what you do to one side, you?

Answer 83

Do to the other

Answer 84

So 8.48?

Answer 85

That seems to be what a is

Answer 86

Now what do you do (:

Answer 87

Plug it in now?

Answer 88

For the area of a square, yes

Answer 89

Technically we could have skipped this if we first discussed the area of a square which is side times side

or....s^2 (:

Answer 90

You will know what I mean once you multiply the sqrt of 72 by the sqrt of 72, lol

Answer 91

It came back as 72?

Answer 92

yes

Answer 93

so??

Answer 94

Yep

Answer 95

Okay thank you so much! haha this wasn't exactly short.

Answer 96

So thanks for bearing with me :)