Question
Find the surface area of a rectangular pyramid with these measurements: l = 8 cm, w = 4 cm, and h = 2 cm. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
The surface area of a rectangular pyramid can be found by adding the area of the base to the sum of the areas of the four triangular faces.
The area of the base is given by the formula: base area = length * width = 8 cm * 4 cm = 32 cm^2.
The area of each triangular face can be found using the formula: face area = (1/2) * base * height. For each face, the base is equal to the length of the rectangle and the height is equal to the height of the pyramid.
The area of the four triangular faces can be calculated as follows:
face 1 area = (1/2) * 8 cm * 2 cm = 8 cm^2
face 2 area = (1/2) * 8 cm * 2 cm = 8 cm^2
face 3 area = (1/2) * 4 cm * 2 cm = 4 cm^2
face 4 area = (1/2) * 4 cm * 2 cm = 4 cm^2
Finally, the surface area of the rectangular pyramid is:
surface area = base area + face 1 area + face 2 area + face 3 area + face 4 area = 32 cm^2 + 8 cm^2 + 8 cm^2 + 4 cm^2 + 4 cm^2 = 56 cm^2.
Therefore, the surface area of the rectangular pyramid is 56 cm^2.
Find the surface area of a rectangular pyramid with these measurements: l = 13 cm, w = 11 cm, and h = 8 cm. Express your answer as a decimal rounded to the nearest hundredth.(1 point)
The surface area of a rectangular pyramid can be found by adding the area of the base to the sum of the areas of the four triangular faces.
The area of the base is given by the formula: base area = length * width = 13 cm * 11 cm = 143 cm^2.
The area of each triangular face can be found using the formula: face area = (1/2) * base * height. For each face, the base is equal to the length of the rectangle and the height is equal to the height of the pyramid.
The area of the four triangular faces can be calculated as follows:
face 1 area = (1/2) * 13 cm * 8 cm = 52 cm^2
face 2 area = (1/2) * 13 cm * 8 cm = 52 cm^2
face 3 area = (1/2) * 11 cm * 8 cm = 44 cm^2
face 4 area = (1/2) * 11 cm * 8 cm = 44 cm^2
Finally, the surface area of the rectangular pyramid is:
surface area = base area + face 1 area + face 2 area + face 3 area + face 4 area = 143 cm^2 + 52 cm^2 + 52 cm^2 + 44 cm^2 + 44 cm^2 = 335 cm^2.
Therefore, the surface area of the rectangular pyramid is 335 cm^2.
What is the surface area of a square pyramid with base length of 10 cm and slant height of 20 cm?(1 point
To find the surface area of a square pyramid, we need to calculate the area of the base and the area of the four triangular faces.
The area of the base is equal to the side length squared, so in this case, it would be 10 cm * 10 cm = 100 cm^2.
To find the area of each triangular face, we will use the formula: (1/2) * base * height, where the base is the side length of the square base and the height is the slant height of the pyramid.
The height of each triangular face can be found using the Pythagorean theorem. Since the slant height is the hypotenuse and the base length is the side of a right triangle, we have:
height = sqrt(slant height squared - (1/2 * base length) squared)
height = sqrt(20 cm^2 - (1/2 * 10 cm)^2)
height = sqrt(20 cm^2 - 5 cm^2)
height = sqrt(15 cm^2)
height = 3.87 cm (rounded to two decimal places).
Now we can calculate the area of each triangular face:
face area = (1/2) * base * height
face area = (1/2) * 10 cm * 3.87 cm
face area ≈ 19.35 cm^2
Since there are four triangular faces, the total area of the triangular faces is 4 * face area = 4 * 19.35 cm^2 = 77.40 cm^2.
Finally, the surface area of the square pyramid is the sum of the base area and the area of the triangular faces:
surface area = base area + total area of triangular faces
surface area = 100 cm^2 + 77.40 cm^2
surface area ≈ 177.40 cm^2.
Therefore, the surface area of the square pyramid is approximately 177.40 cm^2.