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The Lateral Surface Area of a Right Square Pyramid.

 

Examine the following diagram.

 

 

And the following cross section of the pyramid.

 

 

Essentially, what we want to do is take dC and skirt it around the perimeter of the pyramid at a height Y.  The perimeter is simply eight times X.  Notice by similar triangles...

 

The equation of line C using Y-intercept notation...

 

Now integrate the squares of the perimeter (8X) and thickness dC from y = 0 to H

 

 Calculating the lateral surface area of a frustum of a square pyramid is as follows: