aquare pyramid that the base of 40 with the SA equaling 2800
To find the height of the pyramid, let's use the formula for the surface area of a square pyramid:
SA = Base Area + (0.5 × Perimeter of Base × Slant Height)
Given that the base of the pyramid is 40 and the surface area is 2800, we can substitute these values into the formula:
2800 = Base Area + (0.5 × Perimeter of Base × Slant Height)
Since the base is square, the perimeter of the base is 4 times the length of one side:
Perimeter of Base = 4 × Side Length
Perimeter of Base = 4 × 40 = 160
Now we can rewrite the equation:
2800 = Base Area + (0.5 × 160 × Slant Height)
To find the slant height, we need to rearrange the equation:
Slant Height = (2800 - Base Area) / (0.5 × 160)
Since the base is square, the base area is the square of the side length:
Base Area = Side Length^2
Substituting the value for the base:
Base Area = 40^2 = 1600
Now we can calculate the slant height:
Slant Height = (2800 - 1600) / (0.5 × 160)
Slant Height = 1200 / 80
Slant Height = 15
Therefore, the slant height of the pyramid is 15.