Use the formula for surface area of a square pyramid to solve for the slate height at the length of the base is 40 inches and sa equals 2,800 in square
The formula for the surface area (SA) of a square pyramid is given by:
SA = L^2 + 2Lh
where L is the length of the base of the pyramid and h is the height of the pyramid.
In this problem, we are given that L = 40 inches and SA = 2,800 in^2.
Substituting these values into the formula, we have:
2,800 = 40^2 + 2(40)(h)
Simplifying the equation, we get:
2,800 = 1,600 + 80h
Subtracting 1,600 from both sides of the equation, we get:
1,200 = 80h
Dividing both sides of the equation by 80, we get:
h = 15 inches
Therefore, the height of the pyramid is 15 inches.