What is the surface area of a square pyramid where the base edge is 8 ft. and the slant height is 16 ft.? (1 point)
• 512 ft.?
• 256 ft.?
• 128 ft.?
• 320 ft?
The surface area of a square pyramid can be found using the formula:
Surface area = base area + lateral area
First, let's find the base area. Since the base of the pyramid is a square, the base area is equal to the length of one side squared:
Base area = (8 ft)^2 = 64 ft^2
Next, let's find the lateral area. The lateral area of a square pyramid can be found using the formula:
Lateral area = (1/2) * perimeter of base * slant height
Since the base of the pyramid is a square, the perimeter of the base is equal to 4 times the length of one side:
Perimeter of base = 4 * 8 ft = 32 ft
Therefore, the lateral area is:
Lateral area = (1/2) * 32 ft * 16 ft = 256 ft^2
Finally, we can find the total surface area by adding the base area and the lateral area:
Surface area = 64 ft^2 + 256 ft^2 = 320 ft^2
Therefore, the surface area of the square pyramid is 320 ft^2.
So the correct answer is:
• 320 ft?
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. (1 point)
• 52.25 in.?
• 55.75 in.?
• 47.25 in.?
• 58.25 in.?
The surface area of a triangular pyramid can be found using the formula:
Surface area = base area + lateral area
First, let's find the base area. Since the base of the pyramid is a triangle, the base area can be found using the formula for the area of a triangle:
Base area = (1/2) * base length * height of base
Base area = (1/2) * 5 in * 4.3 in = 10.75 in^2
Next, let's find the lateral area. The lateral area of a triangular pyramid can be found using the formula:
Lateral area = (1/2) * perimeter of base * slant height
To find the perimeter of the base, we need to find the lengths of the three sides of the triangle. Since we know the base length is 5 in, we need to find the length of the other two sides.
Using the Pythagorean Theorem, we can find the length of one of the sides:
(3.45)^2 + (4.3)^2 = c^2
11.9025 + 18.49 = c^2
c^2 = 30.3925
c ≈ 5.51 in
Therefore, the length of each side of the triangle is approximately 5.51 in.
The perimeter of the base is then:
Perimeter of base = 5 in + 5.51 in + 5.51 in = 16.02 in
Therefore, the lateral area is:
Lateral area = (1/2) * 16.02 in * 6 in = 48.06 in^2
Finally, we can find the total surface area by adding the base area and the lateral area:
Surface area = 10.75 in^2 + 48.06 in^2 = 58.81 in^2
Therefore, the surface area of the triangular pyramid is 58.81 in^2.
However, none of the provided options match this answer. Thus, none of the options given are correct.
When creating the formula for surface area of a triangular pyramid (SA = zab + 3 (-1b)),
what formula is being used? (1 point)
O area of a triangle
• perimeter
• area of a square
• volume
The formula being used is for the surface area of a triangular pyramid. However, the given formula (SA = zab + 3(-1b)) does not seem to be a correct formula for calculating the surface area. The correct formula for the surface area of a triangular pyramid is:
Surface area = base area + lateral area
So, given the options you provided, none of them accurately represent the formula being used for calculating the surface area of a triangular pyramid.