the surface area of a square pyraid is 116 and the toatal for all four faces is 80 what is he lengghth of one of the sides
Let the length of one side of the square base be x and the height be h.
The surface area of a square pyramid with square base is given by:
S = x^2 + 2x√(x^2/4 + h^2)
Given that the surface area is 116:
116 = x^2 + 2x√(x^2/4 + h^2)
Given that the total for all four faces is 80:
4(x√(x^2/4 + h^2)) = 80
x√(x^2/4 + h^2) = 20
We can substitute x√(x^2/4 + h^2) = 20 into the equation for surface area:
116 = x^2 + 2(20)
116 = x^2 + 40
76 = x^2
x = √76
Therefore, the length of one of the sides is √76.