Find the lateral area the regular pyramid.
L. A. =

Question

Find the lateral area the regular pyramid.
L. A. =

falling_in_katt · Answer

attachment

misssunshinexxoxo · Answer

This is a very awesome tutorial http://www.virtualnerd.com/tutorials/?id=PreAlg_11_01_0031

misssunshinexxoxo · Answer

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.

misssunshinexxoxo · Answer

If you'd like more help; please let me know. Truly feel that tutorial should shine some light

falling_in_katt · Answer

okay

perl · Answer

the base of that pyramid is a hexagon, and a hexagon is made up of 6 equilateral triangles

perl · Answer

If we use this formula  1/2p*L 
We know p = 6*6 
We have to find the slant height L

falling_in_katt · Answer

Wouldn't the slant height be 8?

perl · Answer

8 is the altitude or height of the pyramid

falling_in_katt · Answer

Okay so how do I find the slant height?

perl · Answer

First let's identify the slant height L . I drew it in purple http://prntscr.com/7qqtha

falling_in_katt · Answer

okay

perl · Answer

to find L we can construct a right triangle

perl · Answer

http://prntscr.com/7qqvbz

falling_in_katt · Answer

okay

perl · Answer

we know the leg 8, that is given. the other leg we don't know

falling_in_katt · Answer

correct

perl · Answer

but that leg is the altitude for an equilateral triangle as shown here http://prntscr.com/7qqwob

falling_in_katt · Answer

okay

perl · Answer

and what do we know about equilateral triangles

perl · Answer

an equilateral triangle can be divided into two triangles of 30 60 90 degrees

falling_in_katt · Answer

yes

perl · Answer

the ratio of the sides of a 30 60 90 triangle is $ 1 : \sqrt 3 : 2 $

falling_in_katt · Answer

okay

perl · Answer

|dw:1436461601747:dw|