Question

Solve for the surface area of the square pyramid.
(1 point)
• 299.25 ft.?
O 819 ft.?
• 522 ft.2
• 148.5 ft.?
one side of the base is 15
the length of one side is 9.9

Answer 1

no

Answer 2

To solve for the surface area of the square pyramid, we need to calculate the area of the base and the area of the four triangular faces.

1. Area of the base:
Since the base is square, we can calculate the area by squaring the length of one side:
Area of base = side length^2
Area of base = 15^2
Area of base = 225 ft^2

2. Area of the four triangular faces:
Each face is a triangle with a base equal to the side length of the square base (15 ft) and a height equal to the slant height of the pyramid. The slant height can be calculated using the Pythagorean theorem:
slant height = sqrt((side length/2)^2 + height^2)
slant height = sqrt((15/2)^2 + 9.9^2)
slant height = sqrt(7.5^2 + 9.9^2)
slant height = sqrt(56.25 + 98.01)
slant height = sqrt(154.26)
slant height ≈ 12.42 ft

Now, we can calculate the area of one triangular face and then multiply by 4 to get the total area of the four faces:
Area of one face = (1/2) * base * height
Area of one face = (1/2) * 15 * 12.42
Area of one face ≈ 93.15 ft^2

Total area of the four faces = 4 * 93.15
Total area of the four faces = 372.6 ft^2

3. Adding the areas of the base and the four faces:
Surface area = area of base + area of four faces
Surface area = 225 + 372.6
Surface area = 597.6 ft^2

Therefore, the surface area of the square pyramid is approximately 597.6 square feet.

Answer 3

I apologize for the mistake in my previous calculation.

Let's recalculate the surface area of the square pyramid using the correct formula:

Surface Area = Base Area + (1/2) * Perimeter of Base * Slant Height

1. Base Area:
Area of the square base = side length^2
Area of base = 15^2 = 225 ft^2

2. Perimeter of Base:
Perimeter of base = 4 * side length
Perimeter of base = 4 * 15 = 60 ft

3. Slant Height:
Calculate the slant height using the Pythagorean theorem:
slant height = sqrt((side length/2)^2 + height^2)
slant height = sqrt((15/2)^2 + 9.9^2)
slant height = sqrt(7.5^2 + 98.01)
slant height = sqrt(56.25 + 98.01)
slant height = sqrt(154.26)
slant height ≈ 12.42 ft

4. Surface Area:
Surface Area = 225 + (1/2) * 60 * 12.42
Surface Area = 225 + 372.6
Surface Area = 597.6 ft^2

Therefore, the correct surface area of the square pyramid is 597.6 square feet. Thank you for your patience.