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 inches and SA equals 2800 in^2
The formula for the surface area of a square pyramid is given by:
SA = Base Area + (0.5 * Perimeter of Base * Slant Height)
Given that the surface area (SA) is 2800 in^2 and the base length is 40 inches, we can substitute these values into the formula:
2800 = Base Area + (0.5 * Perimeter of Base * Slant Height)
To find the base area, we need to square the base length:
Base Area = 40^2 = 1600 in^2
Now we can substitute these values back into the equation:
2800 = 1600 + (0.5 * Perimeter of Base * Slant Height)
Now we need to find the perimeter of the base. Since it is a square, the perimeter is given by:
Perimeter of Base = 4 * Base Length = 4 * 40 = 160 inches
Substituting this value back into the equation:
2800 = 1600 + (0.5 * 160 * Slant Height)
Simplifying the equation:
2800 - 1600 = 80 * Slant Height
1200 = 80 * Slant Height
Now, we can solve for the slant height (SH) by dividing both sides of the equation by 80:
Slant Height = 1200 / 80 = 15 inches
Therefore, the slant height of the square pyramid is 15 inches.