what is the surface area of a square pyramid where the base edge is 8 ft and the slant height is 16 ft?
256 ft.^2
320 ft.^2
512 ft.^2
128 ft.^2
To find the surface area of a square pyramid, we need to find the area of the base and the area of the four triangular faces.
The area of the base is given by the formula:
Area of square = (side length)^2
Area of base = (8 ft)^2 = 64 ft^2
Next, we need to find the area of the four triangular faces. Each triangular face is a right triangle and can be found using the formula for the area of a triangle:
Area of triangle = (1/2) * base * height
In this case, the base of each triangular face is equal to the base edge length of the pyramid, which is 8 ft. The height of each triangular face is equal to the slant height of the pyramid, which is 16 ft.
Area of each triangular face = (1/2) * (8 ft) * (16 ft) = 64 ft^2
Since there are four triangular faces, the total area of the four triangular faces is:
Total area of triangular faces = 4 * 64 ft^2 = 256 ft^2
Finally, to find the surface area of the square pyramid, we add the area of the base and the area of the four triangular faces:
Surface area = Area of base + Total area of triangular faces = 64 ft^2 + 256 ft^2 = 320 ft^2
Therefore, the correct answer is 320 ft^2.
To find the surface area of a triangular pyramid, we need to find the area of the base and the area of the three triangular faces.
The area of the base is given by the formula:
Area of triangle = (1/2) * base * height
Area of base = (1/2) * (5 in.) * 4.3 in. = 10.75 in^2
Next, we need to find the area of the three triangular faces. Each triangular face is an isosceles triangle and can be found using the formula for the area of a triangle:
Area of triangle = (1/2) * base * height
In this case, the base of each triangular face is equal to the base of the pyramid, which is 5 in. The height of each triangular face is equal to the slant height of the pyramid, which is 6 in.
Area of each triangular face = (1/2) * (5 in.) * (6 in.) = 15 in^2
Since there are three triangular faces, the total area of the three triangular faces is:
Total area of triangular faces = 3 * 15 in^2 = 45 in^2
Finally, to find the surface area of the triangular pyramid, we add the area of the base and the area of the three triangular faces:
Surface area = Area of base + Total area of triangular faces = 10.75 in^2 + 45 in^2 = 55.75 in^2
Therefore, the correct answer is 55.75 in^2.
The formula S A = 1/2ab + 3 lb is not a commonly used formula for surface area of a triangular pyramid. It seems to be a combination of the formula for the area of a triangle and the formula for the lateral surface area of a rectangular prism (l being the length of the pyramid's base).
The correct formula for the surface area of a triangular pyramid is S A = A b + 1/2P l, where A b is the area of the base, P is the perimeter of the base, and l is the slant height of the pyramid.
A pastry chef is creating a chocolate dessert in the shape of a triangular pyramid. The pyramid has a base of 5 in., the height of the base is 4.3 in., and the slant height is 6 in. Use the correct formula to find the surface area of the chocolate pyramid.
58.25 in^2
55.75 in^2
47.25 in^2
52.25 in^2
when creating the formula for surface area of a triangular pyramid (S A = 1/2ab+3 lb)), what formula is being used?
Area of a triangle
perimeter
area of a square
volume