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Question

http://i53.photobucket.com/albums/g68/je...

For a regular square pyramid, the slant height of each lateral face has a measure equal to that of the edges of the base. If the lateral area is 200 in.^2, find the volume of the pyramid.

Answer 1

4p*p/2=200
so 4p^2=400
and p^2=100 so p=10=the length of one of the sides.
Therefore, the volume is base*height/3
The height is found by considering the right triangle with hypotenuse 10 and base 5; so the height is sqrt(100-25)=sqrt(75)
Finally, the volume is 100*sqrt(75)/3
or, to simplify, 500sqrt(3)/3

Answer 2

Couldn't pull up the picture so I guessed what the diagram was.

Assumed lateral area = base therefore side of base = square root 200 which also then =slant height.

With this info you can draw a vertical cross section hypo=slant height, height of triangle = height of pyramid, base =base side of pyramid.

Use a^2+b^2=c^2 using 1/2 of this cross section
height^2+1/2 base^2=slant height^2
and height =12.24

plug that into pyramid volume equation :Area of the base * Height * 1/3

And get ~817 in ^3 if my math was right