SOLUTION: Please help me so e this question: The surface area of a square pyramid is {{{95 in^2}}} The side length of the base is 5 inches. What is the value of X?

Algebra ->  Surface-area -> SOLUTION: Please help me so e this question: The surface area of a square pyramid is {{{95 in^2}}} The side length of the base is 5 inches. What is the value of X?      Log On


   

Question 973706: Please help me so e this question: The surface area of a square pyramid is 95+in%5E2 The side length of the base is 5 inches. What is the value of X?
Answer by KMST(5328) About Me  (Show Source):
You can put this solution on YOUR website!
What is X? Is it the slant height of the pyramid? Or is it the height of the pyramid?
A right square pyramid is a pyramid with a square base,
and four triangular faces meeting at a vertex that is exactly above the center of the base.
The four triangular faces are congruent (same shape and size).
The distance from the base to the vertex of the pyramid is the height of the pyramid.
The distance from the vertex to each side of the base
(the height of the isosceles triangle that is one of those four triangular faces)
is called the slant height of the pyramid.
The total surface area of a pyramid is the area of the base plus the lateral area (the area of the four triangular faces).
If the side length of the base of a square pyramid is 5 inches,
the surface area of the square base is 25 square inches:
%285inch%29%2A%285inch%29=25inch%5E2 .
If the total surface area of the square pyramid in the problem is 95inch%5E2 ,
and the base surface area is 25inch%5E2 ,
the lateral area is 95inch%5E2-25inch%5E2=70inch%5E2 .
The area of each triangular face is the length of the side of the base, times the slant height, and divided by 2.
For this problem, that area of one triangular face is %285inches%29%2Aslant_height%2F2 ,
and the area of all 4 triangular faces is
4%2A%28%285inches%29%2Aslant_height%2F2%29=70inch%5E2 .
So %284%2A%285inches%29%2F2%29%2Aslant_height=70inch%5E2--->%2810inches%29%2Aslant_height=70inch%5E2--->slant_height=70inch%5E2%2F%2210+inch%22--->slant_height=7inch .