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# what does L.A meam

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Whats L.A when your trying to find surface area of a square-based pyramid?

Guest Apr 12, 2017
#1
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LA stands for "lateral area."

Lateral area is the surface area except for the area of the base.

The lateral area of a pyramid = (1/2) * (perimeter of base) * (height)

hectictar  Apr 12, 2017
#2
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Thanks guest

Could you please derive that formula ?

(My question is only intended for the guest who posted the formula)

Melody  Apr 12, 2017
edited by Melody  Apr 12, 2017
#4
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I am sorry what I said is actually not good, I should have said slant height...

But here is my explanation. You can see how that it is because if you take the triangles and lay them out like this:

Since the base of each triangle is the same length,

area of one blue triange = (1/2)(1/4 * perimeter of base)(slant height)

There are 4 triangles total that area all the same size.. so,

area of all blue triangles = 4 * (1/2)(1/4 * perimeter of base)(slant height)

area of all blue triangles = (1/2)(perimeter of base)(slant height)

hectictar  Apr 12, 2017
edited by hectictar  Apr 12, 2017
#3
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"L.A" of a square-based pyramid

We have four triangles each with base edge "b"   and a slant height, "h"

And....the lateral surface area  =

4 * (1/2) b * h   =

2bh

But.....the perimeter  = 4b

So

2bh  =

(1/2) 4b * h  =

(1/2) *perimeter * slant height of each face

CPhill  Apr 12, 2017