Use the formula for the surface area of a square pyramid to solve for the slant height if the length of the base is 40 in. and SA equals 2,800 in2 .
The formula for the surface area (SA) of a square pyramid is:
SA = B + (1/2)Psl
where B is the area of the base, P is the perimeter of the base, s is the slant height, and l is the length of one side of the base.
Given that the length of the base (l) is 40 in. and the SA is 2,800 in2, we can write the equation as:
2,800 = 40^2 + (1/2)(40)(4s)
Simplifying the equation, we get:
2,800 = 1,600 + 80s
Subtracting 1,600 from both sides, we have:
1,200 = 80s
Dividing both sides by 80, we get:
s = 15
Therefore, the slant height of the square pyramid is 15 in.