a square pyramids dimensions are 9.9 ft and 15 ft
Solve for the surface area of the square pyramid
To find the surface area of a square pyramid, you need to calculate the area of the square base and the area of each triangular face and then add them all together.
Area of the square base:
Side length of the square base = 9.9 ft
Area of the square base = side length squared = (9.9 ft)^2 = 98.01 sq ft
Area of each triangular face:
To find the area of each triangular face, we first need to find the slant height of the pyramid. The slant height can be found using the Pythagorean theorem:
Slant height = √( (1/2 * side length)^2 + height^2 )
Slant height = √( (1/2 * 9.9 ft)^2 + 15 ft)^2 )
Slant height = √( (4.95 ft)^2 + 15 ft)^2 )
Slant height = √( (24.5025 ft) + 225 ft)^2 )
Slant height = √(249.5025 ft)
Slant height ≈ 15.8 ft
Now we can find the area of each triangular face using the formula: 0.5 * base * height
Area of each triangular face = 0.5 * 9.9 ft * 15.8 ft ≈ 78.21 sq ft
Now we can find the surface area of the pyramid by adding up the area of the base and the area of the four triangular faces:
Surface area = Area of base + 4 * Area of each triangular face
Surface area = 98.01 sq ft + 4 * 78.21 sq ft
Surface area = 98.01 sq ft + 312.84 sq ft
Surface area = 410.85 sq ft
Therefore, the surface area of the square pyramid is approximately 410.85 sq ft.
the options are
148.5ft
819ft
522ft
299.25ft
I apologize for the error in my previous calculation. Let's correct it:
Given the dimensions of the square pyramid:
Base side length = 9.9 ft
Slant height = 15 ft
Height = ?
Using the Pythagorean theorem to find the height:
height = sqrt(slant height^2 - (base side length/2)^2)
height = sqrt(15^2 - (9.9/2)^2)
height = sqrt(225 - 24.5025)
height = sqrt(200.4975)
height ≈ 14.15 ft
Now, let's calculate the surface area of the square pyramid:
1. Area of the base (square):
Area_base = side length^2
Area_base = 9.9^2
Area_base = 98.01 sq ft
2. Area of each triangular face:
Area_triangle = 0.5 * base * height
Area_triangle = 0.5 * 9.9 * 15
Area_triangle = 74.25 sq ft
3. Total surface area:
Surface_area = Area of base + 4 * Area of each triangular face
Surface_area = 98.01 + 4*(74.25)
Surface_area = 98.01 + 297
Surface_area = 395.01 sq ft
Therefore, the correct surface area of the square pyramid is approximately 395.01 sq ft.
Given the options provided, the closest result is 299.25 ft.