Question

Saul for the surface area of the square pyramid with the base 15 feet and the side 9.9 feet

Answer 1

The surface area of a square pyramid can be calculated using the formula:

Surface Area = Base Area + (0.5 * Perimeter of Base * Slant Height)

First, we need to find the base area of the square pyramid. Since the base is a square, we can use the formula for the area of a square:

Base Area = side^2 = 15^2 = 225 square feet

Next, we calculate the perimeter of the base:

Perimeter of Base = 4 * side = 4 * 15 = 60 feet

Now we need to find the slant height of the pyramid. The slant height can be found using the Pythagorean theorem with half the diagonal of the base square and the height of the pyramid:

Diagonal of Base = side * sqrt(2) = 15 * sqrt(2) ≈ 21.21 feet

Slant Height = sqrt((Diagonal of Base/2)^2 + height^2)
Slant Height = sqrt((21.21/2)^2 + 9.9^2)
Slant Height = sqrt(142.84 + 98.01)
Slant Height ≈ sqrt(240.85)
Slant Height ≈ 15.52 feet

Lastly, we can plug in all the values into the surface area formula:

Surface Area = 225 + (0.5 * 60 * 15.52)
Surface Area = 225 + (30 * 15.52)
Surface Area = 225 + 465.6
Surface Area = 690.6 square feet

Therefore, the surface area of the square pyramid is approximately 690.6 square feet.