To find the surface area of a rectangular pyramid, we need to calculate the area of the base and the area of the three triangular faces.
1. Area of the base:
Area of the base = length * width
Area = 8 yd * 4 yd = 32 square yards
2. Area of the three triangular faces:
Each triangular face is a right triangle with base and height equal to the rectangle's dimensions.
Area of one triangular face = (1/2) * base * height
Area = (1/2) * 8 yd * 2 yd = 8 square yards
Total surface area = Area of the base + 3 * Area of one triangular face
Total surface area = 32 square yards + 3 * 8 square yards
Total surface area = 32 square yards + 24 square yards
Total surface area = 56 square yards
Therefore, the surface area of the rectangular pyramid is 56 square yards.
Find the surface area of a rectangular pyramid with these measurements: l = 8 yd, w = 4 yd, and h = 2 yd.
(1 point)
5 answers
incorrect.
I apologize for the mistake. Let's correct it:
To find the surface area of a rectangular pyramid, we calculate the sum of the area of the base and the area of the three lateral faces.
1. Area of the base:
Area = length * width
Area = 8 yd * 4 yd = 32 square yards
2. Area of each triangular face:
We need to find the slant height of the pyramid using the Pythagorean theorem:
slant height = sqrt((0.5 * base)^2 + height^2) = sqrt((4^2) + (2^2)) = sqrt(16 + 4) = sqrt(20) = 2sqrt(5) yd
Now, we can find the area of each triangular face using the formula:
Area = 0.5 * base * slant height
Area = 0.5 * 4 yd * 2sqrt(5) yd = 4sqrt(5) square yards for each face
3. Calculate the total surface area:
Total surface area = Area of the base + 3 * Area of one triangular face
Total surface area = 32 square yards + 3 * 4sqrt(5) square yards
Total surface area = 32 square yards + 12sqrt(5) square yards
Total surface area ≈ 54.72 square yards
Therefore, the surface area of the rectangular pyramid with the given measurements is approximately 54.72 square yards.
To find the surface area of a rectangular pyramid, we calculate the sum of the area of the base and the area of the three lateral faces.
1. Area of the base:
Area = length * width
Area = 8 yd * 4 yd = 32 square yards
2. Area of each triangular face:
We need to find the slant height of the pyramid using the Pythagorean theorem:
slant height = sqrt((0.5 * base)^2 + height^2) = sqrt((4^2) + (2^2)) = sqrt(16 + 4) = sqrt(20) = 2sqrt(5) yd
Now, we can find the area of each triangular face using the formula:
Area = 0.5 * base * slant height
Area = 0.5 * 4 yd * 2sqrt(5) yd = 4sqrt(5) square yards for each face
3. Calculate the total surface area:
Total surface area = Area of the base + 3 * Area of one triangular face
Total surface area = 32 square yards + 3 * 4sqrt(5) square yards
Total surface area = 32 square yards + 12sqrt(5) square yards
Total surface area ≈ 54.72 square yards
Therefore, the surface area of the rectangular pyramid with the given measurements is approximately 54.72 square yards.
still wrong
Find the surface area of a rectangular pyramid with these measurements: l = 8 yd, w = 4 yd, and h = 2 yd.
43.31 yd.²
72.52 yd.²
66 yd.²
55.55 yd.²
Find the surface area of a rectangular pyramid with these measurements: l = 8 yd, w = 4 yd, and h = 2 yd.
43.31 yd.²
72.52 yd.²
66 yd.²
55.55 yd.²
To find the surface area of a rectangular pyramid with given measurements, we calculate the area of the base and the three triangular faces.
1. Area of the base:
Area of the base = length * width
Area = 8 yd * 4 yd = 32 square yards
2. Area of each triangular face:
The triangular face is a right triangle with base and height equal to the rectangle's dimensions. To calculate the slant height, we use the Pythagorean theorem:
slant height = sqrt((0.5 * base)^2 + height^2) = sqrt((4^2) + (2^2)) = sqrt(16 + 4) = sqrt(20) = 2sqrt(5) yd
Now, we can find the area of each triangular face using the formula:
Area = 0.5 * base * slant height
Area = 0.5 * 4 yd * 2sqrt(5) yd = 4sqrt(5) square yards for each face
3. Calculate the total surface area:
Total surface area = Area of the base + 3 * Area of one triangular face
Total surface area = 32 square yards + 3 * 4sqrt(5) square yards
Total surface area = 32 square yards + 12sqrt(5) square yards
Now, calculating the actual value of the total surface area:
Total surface area ≈ 32 + 12 * 2.236 ≈ 32 + 26.83 ≈ 58.83 square yards
Therefore, the correct answer is closest to 55.55 yd².
1. Area of the base:
Area of the base = length * width
Area = 8 yd * 4 yd = 32 square yards
2. Area of each triangular face:
The triangular face is a right triangle with base and height equal to the rectangle's dimensions. To calculate the slant height, we use the Pythagorean theorem:
slant height = sqrt((0.5 * base)^2 + height^2) = sqrt((4^2) + (2^2)) = sqrt(16 + 4) = sqrt(20) = 2sqrt(5) yd
Now, we can find the area of each triangular face using the formula:
Area = 0.5 * base * slant height
Area = 0.5 * 4 yd * 2sqrt(5) yd = 4sqrt(5) square yards for each face
3. Calculate the total surface area:
Total surface area = Area of the base + 3 * Area of one triangular face
Total surface area = 32 square yards + 3 * 4sqrt(5) square yards
Total surface area = 32 square yards + 12sqrt(5) square yards
Now, calculating the actual value of the total surface area:
Total surface area ≈ 32 + 12 * 2.236 ≈ 32 + 26.83 ≈ 58.83 square yards
Therefore, the correct answer is closest to 55.55 yd².
1 answer