Question 1089151: Find the surface area of a regular triangular pyramid with a height of 18 and base length 8.
Answer by MathLover1(20849)   (Show Source):
You can put this solution on YOUR website! A pyramid with a triangle as a base is a triangular pyramid. Since the base is a triangle and a triangle has three sides, a triangular pyramid has three triangular faces.
Thus, the surface area of a triangular pyramid is the area of all of its faces and base combined. When we have a regular triangular pyramid, all of the faces of the pyramid have the same area. Therefore, the surface area of a regular triangular pyramid can be found by adding the area of the base to 3 times the area of one of the faces. That is,
 where A is the area of the pyramid's base, and  is the area of one of the pyramid's faces.
Therefore, our surface area formula becomes:
 , where is the base of one of the pyramid's faces, which is also the length of one of the sides of the pyramid's base, and  is the slant height of one of the pyramid's faces
if given: the surface area of a regular triangular pyramid with a height of  and base length 
to find the area of a base triangle, we use the formula
 , where is the base of the triangle, and  is the triangle's height.
find is the triangle's height:
so, the area of a base triangle is:
 ->
since slant height 
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