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 S A equals 2,800 in^2.
The formula for the surface area of a square pyramid is given by:
SA = Base Area + (1/2) * Perimeter of Base * Slant Height
The base area of a square pyramid is given by the formula:
Base Area = (Length of Base)^2
Given that the length of the base is 40 inches, the base area can be calculated as:
Base Area = (40)^2 = 1600 square inches
Substituting the given values into the surface area formula:
2800 = 1600 + (1/2) * Perimeter of Base * Slant Height
We need to find the perimeter of the base in order to solve for the slant height. Since it is a square pyramid, the perimeter of the base is given by:
Perimeter of Base = 4 * Length of Base
Substituting the length of the base:
Perimeter of Base = 4 * 40 = 160 inches
Now we can solve the equation:
2800 = 1600 + (1/2) * 160 * Slant Height
Subtracting 1600 from both sides:
2800 - 1600 = (1/2) * 160 * Slant Height
1200 = 80 * Slant Height
Dividing both sides by 80:
1200/80 = Slant Height
15 = Slant Height
Therefore, the slant height of the square pyramid is 15 inches.