anonymous
  • anonymous
Help!! I give medals Find the following: Slant height l, Base perimeter P, Base area B, Lateral area, and Surface area S
Mathematics
  • Stacey Warren - Expert brainly.com
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katieb
  • katieb
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anonymous
  • anonymous
|dw:1370303183800:dw|
anonymous
  • anonymous
@eSpeX is this kinda like the other one I did??
eSpeX
  • 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
  • ganeshie8
you need to fold it a bit, and then work
eSpeX
  • 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
  • eSpeX
What are the measurements you are given, and what are the relevant formulas for each of the 5 tasks?
anonymous
  • 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
  • eSpeX
Wow, where are you getting your formulas? For perimeter, is that \[\frac{(s-b)}{\frac{1}{2}*l}\]?
anonymous
  • anonymous
No\[(s-b) \div \frac{ 1 }{ 2 } \times l\]
eSpeX
  • 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
  • anonymous
so the perimeter is 8?
eSpeX
  • eSpeX
Yes
anonymous
  • anonymous
Ok are the rest of the fromulas I gave you right?
eSpeX
  • 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
  • anonymous
Ok how do I do the \[2\sqrt{2}\] I get confused whe square root is involved
eSpeX
  • eSpeX
For your surface area, S, your equation should be \(\frac{1}{2}Pl+B\)
eSpeX
  • eSpeX
You will simply square your 2 and your \(\sqrt{2}\)
eSpeX
  • eSpeX
So answer this, what is 2 squared? what is \(\sqrt{2}\) squared?
anonymous
  • anonymous
\[4\sqrt{4}\]
eSpeX
  • eSpeX
Right, now can you think of another way to represent 4?
anonymous
  • anonymous
i don't understand your question
eSpeX
  • 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
  • anonymous
2+2=4 or are you looking for a fraction
eSpeX
  • eSpeX
I was thinking more of a power.
anonymous
  • anonymous
ooh 4^2
eSpeX
  • eSpeX
Close, but 4^2 is 16, we want a square that equals 4
anonymous
  • anonymous
2^2
eSpeX
  • eSpeX
Exactly. So now you have \(4\sqrt{2{^2}}\)
eSpeX
  • eSpeX
And what happens when you take the square of a square root?
anonymous
  • anonymous
it goes away
eSpeX
  • eSpeX
Yes, excellent.
eSpeX
  • eSpeX
So you now have 4*2
anonymous
  • anonymous
so then would the lant heigh be 7
eSpeX
  • eSpeX
Remember that this is all under a radical still. \[\sqrt{4\sqrt{2^2}-1^2}\rightarrow\sqrt{4*2-1^2}\]
anonymous
  • anonymous
so 2.64
eSpeX
  • eSpeX
Yes. Or just leave it as \(\sqrt{7}\)
anonymous
  • anonymous
Ok so now how do you find the base area
eSpeX
  • eSpeX
Remember that the base is just a square with leg length of 2.
eSpeX
  • eSpeX
So far you know: P = 8 l = 2.65 or \(\sqrt{7}\)
anonymous
  • anonymous
Ok
eSpeX
  • eSpeX
How do you find the area of a square, which is the base (B) of our pyramid?
anonymous
  • anonymous
A=s^2
eSpeX
  • eSpeX
Exactly, remembering that (side)^2 only works for a square, otherwise we use length*width.
eSpeX
  • eSpeX
What values do you know now?
anonymous
  • anonymous
so is the base area 4 we kno the slant heigh and the base perimeter
eSpeX
  • 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
  • anonymous
1/2 (8*2.65
eSpeX
  • eSpeX
Exactly
anonymous
  • anonymous
i get 21.2 divide that in half lateral area=10.6
eSpeX
  • eSpeX
Nice work, only one more to go. :)
eSpeX
  • 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
  • eSpeX
Remember that you already calculated the first part of that equation.
anonymous
  • anonymous
i get 12.6 for surface area
eSpeX
  • eSpeX
QED, you did it. :) Good job.
anonymous
  • anonymous
Thank you so much for yor help i appreate it
eSpeX
  • eSpeX
Oh wait, check that. You sure about that surface area?
eSpeX
  • eSpeX
B was the area of the base
anonymous
  • anonymous
i had 21.2+4=25.2/in half and i get 12.6
eSpeX
  • eSpeX
You must follow your order of operations, PEMDAS, in which case you would leave the addition for last.
anonymous
  • anonymous
so i take 2.65+4=6.65*8=53.2 diveid that in half and i get 26.6
anonymous
  • anonymous
that is so complacated
eSpeX
  • 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
  • anonymous
Ok i get it thanks so much fer the help
eSpeX
  • eSpeX
You're welcome.

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