Find the surface area of a rectangular pyramid with these measurements: l = 8 yd., w = 4 yd., and h = 2 yd.(1 point) Responses 72.52 yd.^2
66 yd.^2
43.31 yd.^2
55.55 yd.^2
To find the surface area of a rectangular pyramid, we need to find the area of each of the four triangular faces and the base.
The area of each triangular face can be found using the formula: (1/2) * base * height. The base of each triangular face is given by the length and width of the rectangular base, which are 8 yd. and 4 yd. The height of each triangular face is given by the height of the pyramid, which is 2 yd.
The area of each triangular face is therefore: (1/2) * 8 yd. * 2 yd. = 8 yd.^2
Since there are four triangular faces, the total area of the triangular faces is: 4 * 8 yd.^2 = 32 yd.^2
The area of the rectangular base is given by the formula: length * width = 8 yd. * 4 yd. = 32 yd.^2
The total surface area of the rectangular pyramid is the sum of the areas of the triangular faces and the base: 32 yd.^2 + 32 yd.^2 = 64 yd.^2
Therefore, the correct answer is: 64 yd.^2
That's not an answer
Apologies for the confusion. Let's calculate the surface area again.
The area of each triangular face can be found using the formula: (1/2) * base * height. The base of each triangular face is given by the length and width of the rectangular base, which are 8 yd. and 4 yd. The height of each triangular face is given by the height of the pyramid, which is 2 yd.
The area of each triangular face is therefore: (1/2) * 8 yd. * 2 yd. = 8 yd.^2
Since there are four triangular faces, the total area of the triangular faces is: 4 * 8 yd.^2 = 32 yd.^2
The area of the rectangular base is given by the formula: length * width = 8 yd. * 4 yd. = 32 yd.^2
The total surface area of the rectangular pyramid is the sum of the areas of the triangular faces and the base: 32 yd.^2 + 32 yd.^2 = 64 yd.^2
Therefore, the correct answer is: 64 yd.^2
Use the formula for the surface area of a square pyramid to find the surface area if the base edge length is 5 yards and the height is 25 yards. Round to the nearest whole number.(1 point) Responses 1,298 square yards 1,298 square yards 276 square yards 276 square yards 251 square yards 251 square yards 151 square yards
The surface area of a square pyramid can be calculated using the formula:
Surface Area = base area + (1/2) * perimeter * slant height
First, let's calculate the base area. Since the pyramid's base is a square, the area is given by the formula: length * width. In this case, the length is 5 yards, so the base area is 5 yards * 5 yards = 25 square yards.
Next, we need to calculate the slant height. In a square pyramid, the slant height can be found using the formula: slant height = √(height^2 + (base edge/2)^2). Plugging in the values, we get: slant height = √(25 yards^2 + (5 yards/2)^2) = √(625 + 6.25) = √631.25 ≈ 25.12 yards.
Now we can calculate the surface area: Surface Area = 25 square yards + (1/2) * perimeter * 25.12 yards.
The perimeter of the base is equal to 4 times the length of one side, so in this case: perimeter = 4 * 5 yards = 20 yards.
Plugging in the values, we get: Surface Area = 25 square yards + (1/2) * 20 yards * 25.12 yards ≈ 25 square yards + 10 * 25.12 square yards ≈ 25 square yards + 251.2 square yards ≈ 276.2 square yards.
Rounding to the nearest whole number, the surface area is approximately 276 square yards.
Therefore, the correct answer is 276 square yards.
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) Responses 512 ft.2512 ft. squared 256 ft.2256 ft. squared 128 ft.2 128 ft. squared 320 ft.2
To find the surface area of a square pyramid, we need to find the sum of the areas of the base and the four triangular faces.
1. The area of the base can be found using the formula: side length^2. In this case, the base edge is 8 ft., so the area of the base is 8 ft. * 8 ft. = 64 ft.²
2. The area of each triangular face can be found using the formula: (1/2) * base * height. The base of each triangular face is given by the base edge, which is 8 ft. The height of each triangular face is given by the slant height, which is 16 ft.
The area of each triangular face is therefore: (1/2) * 8 ft. * 16 ft. = 64 ft.²
Since there are four triangular faces, the total area of the triangular faces is: 4 * 64 ft.² = 256 ft.²
3. Finally, we add the area of the base and the area of the triangular faces to find the surface area of the square pyramid:
Surface Area = area of base + area of triangular faces
Surface Area = 64 ft.² + 256 ft.² = 320 ft.²
Therefore, the correct answer is 320 ft.².