Falling_In_Katt
  • Falling_In_Katt
Find the lateral area the regular pyramid. L. A. =
Geometry
  • Stacey Warren - Expert brainly.com
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SOLVED
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chestercat
  • chestercat
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Falling_In_Katt
  • Falling_In_Katt
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misssunshinexxoxo
  • misssunshinexxoxo
This is a very awesome tutorial http://www.virtualnerd.com/tutorials/?id=PreAlg_11_01_0031
misssunshinexxoxo
  • misssunshinexxoxo
The lateral area of a regular pyramid is 1/2p*l where p is the perimeter of the base and l is the slant height. The lateral formula for a cone is also 1/2p*l where p is the perimeter (or in this case the circumference) of the base and l is the slant height. It can also be shown as pi*r*l, where r is the radius of the base, or 1/2pi*d*l, where d is the diameter of the radius of the base. However, note that this is only the lateral area formula for a right cone. There can be many formulas for the lateral area of an oblique cone. And what they mean when they say they want the answer in terms of pi is that they do not want you to do any process to it. They want the pi to be in the answer. For example, instead of multiplying 3*pi, the answer would instead be 3pi. Or instead of adding 3 + pi, the answer would actually be 3 + pi.

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misssunshinexxoxo
  • misssunshinexxoxo
If you'd like more help; please let me know. Truly feel that tutorial should shine some light
Falling_In_Katt
  • Falling_In_Katt
okay
perl
  • perl
the base of that pyramid is a hexagon, and a hexagon is made up of 6 equilateral triangles
perl
  • perl
If we use this formula 1/2p*L We know p = 6*6 We have to find the slant height L
Falling_In_Katt
  • Falling_In_Katt
Wouldn't the slant height be 8?
perl
  • perl
8 is the altitude or height of the pyramid
Falling_In_Katt
  • Falling_In_Katt
Okay so how do I find the slant height?
perl
  • perl
First let's identify the slant height L . I drew it in purple http://prntscr.com/7qqtha
Falling_In_Katt
  • Falling_In_Katt
okay
perl
  • perl
to find L we can construct a right triangle
perl
  • perl
http://prntscr.com/7qqvbz
Falling_In_Katt
  • Falling_In_Katt
okay
perl
  • perl
we know the leg 8, that is given. the other leg we don't know
Falling_In_Katt
  • Falling_In_Katt
correct
perl
  • perl
but that leg is the altitude for an equilateral triangle as shown here http://prntscr.com/7qqwob
Falling_In_Katt
  • Falling_In_Katt
okay
perl
  • perl
and what do we know about equilateral triangles
perl
  • perl
an equilateral triangle can be divided into two triangles of 30 60 90 degrees
Falling_In_Katt
  • Falling_In_Katt
yes
perl
  • perl
the ratio of the sides of a 30 60 90 triangle is \( 1 : \sqrt 3 : 2 \)
Falling_In_Katt
  • Falling_In_Katt
okay
perl
  • perl
|dw:1436461601747:dw|
perl
  • perl
the height of this triangle is the leg we need
Falling_In_Katt
  • Falling_In_Katt
okay
perl
  • perl
so we need 3 : h : 6 to have same ratio as 1 : sqrt(3) : 2
perl
  • perl
3 : 3 √3 : 6 works
perl
  • perl
if you divide through by 3, you get 1 : √3 : 2
Falling_In_Katt
  • Falling_In_Katt
Is 3 the height?
perl
  • perl
3√3 is the height
perl
  • perl
|dw:1436462137479:dw|
Falling_In_Katt
  • Falling_In_Katt
So I would do \[\frac{ 1 }{ 2 }(6*6)(3\sqrt{3})\]
perl
  • perl
almost, now we have to L
Falling_In_Katt
  • Falling_In_Katt
oh okay
perl
  • perl
http://prntscr.com/7qr6c4
perl
  • perl
We can use pythagorean theorem to find L
perl
  • perl
8^2 + ( 3 √ 3)^2 = L^2
Falling_In_Katt
  • Falling_In_Katt
91?
perl
  • perl
correct, that would be L^2 take the square root of that
perl
  • perl
L^2 = 91 L = sqrt(91)
perl
  • perl
So the lateral area will be $$\Large \frac{ 1 }{ 2 }(6*6)(\sqrt{91})$$
perl
  • perl
I hope that was clear.
Falling_In_Katt
  • Falling_In_Katt
Thank you!

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