Help!! I give medals
Find the following: Slant height l, Base perimeter P, Base area B, Lateral area, and Surface area S

- anonymous

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- anonymous

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- anonymous

@eSpeX is this kinda like the other one I did??

- eSpeX

This is like a compilation of the last 3 you have done. You are asked to find just about every area imaginable. :)

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- ganeshie8

you need to fold it a bit, and then work

- eSpeX

It might be easier to break it out into tasks:
Find the following:
Slant height l
Base perimeter P
Base area B
Lateral area
Surface area S

- eSpeX

What are the measurements you are given, and what are the relevant formulas for each of the 5 tasks?

- anonymous

the measurments are given in the pic
P=(s-B)/ 1/2xl
LA=1/2(Pxl)
B=lw
Slan hight=h^2b^2
Sa=2 area of bacse

- eSpeX

Wow, where are you getting your formulas? For perimeter, is that \[\frac{(s-b)}{\frac{1}{2}*l}\]?

- anonymous

No\[(s-b) \div \frac{ 1 }{ 2 } \times l\]

- eSpeX

In this context, you are given 'l' as the slant height. Therefore, P=4*2, because they are defining P as the perimeter of the base, which is a square.

- anonymous

so the perimeter is 8?

- eSpeX

Yes

- anonymous

Ok are the rest of the fromulas I gave you right?

- eSpeX

The slant height, you have it laid out right by making a right triangle in one of the faces and using the Pythagorean theorem. If the measurements you were given are the \(2\sqrt{2}\) and the \(2\), then you will have a slant height equal to:\[\sqrt{(2\sqrt{2})^2-1^2}= l\]

- anonymous

Ok how do I do the \[2\sqrt{2}\]
I get confused whe square root is involved

- eSpeX

For your surface area, S, your equation should be \(\frac{1}{2}Pl+B\)

- eSpeX

You will simply square your 2 and your \(\sqrt{2}\)

- eSpeX

So answer this,
what is 2 squared?
what is \(\sqrt{2}\) squared?

- anonymous

\[4\sqrt{4}\]

- eSpeX

Right, now can you think of another way to represent 4?

- anonymous

i don't understand your question

- eSpeX

If I have a 4 on the paper, what else can I write that would equal the same value? Preferably something that I could use to cancel out the root.

- anonymous

2+2=4
or are you looking for a fraction

- eSpeX

I was thinking more of a power.

- anonymous

ooh 4^2

- eSpeX

Close, but 4^2 is 16, we want a square that equals 4

- anonymous

2^2

- eSpeX

Exactly. So now you have \(4\sqrt{2{^2}}\)

- eSpeX

And what happens when you take the square of a square root?

- anonymous

it goes away

- eSpeX

Yes, excellent.

- eSpeX

So you now have 4*2

- anonymous

so then would the lant heigh be 7

- eSpeX

Remember that this is all under a radical still. \[\sqrt{4\sqrt{2^2}-1^2}\rightarrow\sqrt{4*2-1^2}\]

- anonymous

so 2.64

- eSpeX

Yes. Or just leave it as \(\sqrt{7}\)

- anonymous

Ok so now how do you find the base area

- eSpeX

Remember that the base is just a square with leg length of 2.

- eSpeX

So far you know:
P = 8
l = 2.65 or \(\sqrt{7}\)

- anonymous

Ok

- eSpeX

How do you find the area of a square, which is the base (B) of our pyramid?

- anonymous

A=s^2

- eSpeX

Exactly, remembering that (side)^2 only works for a square, otherwise we use length*width.

- eSpeX

What values do you know now?

- anonymous

so is the base area 4
we kno the slant heigh and the base perimeter

- eSpeX

Now let's find the lateral area
Slant height l = 2.65 or \(\sqrt{7}\)
Base perimeter P = 8
Base area B = 4
Lateral area = \(\frac{1}{2}P*l\)
Surface area S

- anonymous

1/2 (8*2.65

- eSpeX

Exactly

- anonymous

i get 21.2 divide that in half lateral area=10.6

- eSpeX

Nice work, only one more to go. :)

- eSpeX

Now let's find the surface area
Slant height l = 2.65 or \(\sqrt{7}\)
Base perimeter P = 8
Base area B = 4
Lateral area = 10.6
Surface area S = \(\frac{1}{2}P*l + B\)

- eSpeX

Remember that you already calculated the first part of that equation.

- anonymous

i get 12.6 for surface area

- eSpeX

QED, you did it. :) Good job.

- anonymous

Thank you so much for yor help i appreate it

- eSpeX

Oh wait, check that. You sure about that surface area?

- eSpeX

B was the area of the base

- anonymous

i had 21.2+4=25.2/in half and i get 12.6

- eSpeX

You must follow your order of operations, PEMDAS, in which case you would leave the addition for last.

- anonymous

so i take 2.65+4=6.65*8=53.2 diveid that in half and i get 26.6

- anonymous

that is so complacated

- eSpeX

\(\frac{1}{2}P*l\) was just your lateral area, so if you then have \(\frac{1}{2}P*l+B\) can you see where you will simply take your lateral area and add your base area? :)

- anonymous

Ok i get it thanks so much fer the help

- eSpeX

You're welcome.

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