Okay. The surface area of a square pyramid is a square and 4 triangles.
First, find the area of the square:
5*5=25
Subtract the square from the entire surface area:
175-25=150
Now, we know that the area of the triangles added together is 150. Since there are 4 triangles, we want to find the area of one triangle:
150/4=37.5
Now we can set up an equation to find the slant height (or the height of the triangle):
1/2*5*h=37.5
5h=75
h=15
The slant height is 37.5 inches. Sorry for the long answer!