How do you find the area of a pyramid?
Student asking
grade 10
My name is Lisa
Hi Lisa
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 s^{2} = h^{2} + (a/2)^{2}. Thus if you know a and s you can find h = Sqrt(s^{2}-(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). |
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