Destroyer QR 104

[simplyome]

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So I have a question, what the heck is the area of a pyramid?

If they are talking surface area wouldn't you count the base also?? If so the answer isn't listed.

But solution doesn't count base so I am not sure.

 

[DrKimkim]

Don't worry I had the same problem, but they forgot to put the base you have to add the surface area of the base (A squared) to the answer key!

 

[DrKimkim]

To find the surface area of a pyramid with a square base as in the diagram you need to add the area of the base and the areas of the four triangular faces. If |AB| = |BC| = |CD| = |DA| = a then the area of the base is a 2 square units. If you know the "slant height" |BP| = s of the pyramid then to find the area of the face PBC you need its height h = |PR|.

Since PBR is a right triangle the theorem of Pythagoras tells us that s2 = h2 + (a/2)2. Thus if you know a and s you can find h = Sqrt(s2-(a/2)2) and the area of PBR which is 1/2 bxh. Thus the surface area of the pyramid is a 2+4(1/2 bxh).