To find the surface area of a rectangular pyramid, we need to find the area of each of the five faces and then sum them up.
1. The base of the pyramid is a rectangle with dimensions 8 yd. by 4 yd.
Area of base = l x w = 8 yd x 4 yd = 32 yd^2
2. There are four triangular faces on a rectangular pyramid. Each triangle has a base equal to the width of the base and height of the pyramid as one of its sides. The other two sides of the triangle are the slant height of the pyramid.
Slant height can be found using Pythagoras theorem:
s = sqrt((w/2)^2 + h^2)
s = sqrt((4/2)^2 + 2^2) = sqrt(2^2 + 4) = sqrt(4 + 4) = sqrt(8) = 2.83 yd
Now, we can calculate the area of each triangular face:
Area of each triangular face = 1/2 x base x height = 1/2 x 4 yd x 2.83 yd = 5.66 yd^2
3. The total surface area is the sum of areas of the base and the four triangular faces:
Surface area = area of base + 4 x area of triangular face
Surface area = 32 yd^2 + 4 x 5.66 yd^2 = 32 yd^2 + 22.64 yd^2 = 54.64 yd^2
Therefore, the surface area of the rectangular pyramid is 54.64 square yards.
Find the surface area of a rectangular pyramid with these measurements:
l = 8 yd., w = 4 yd., and h = 2 yd.
5 answers
Wrong what's the real answer
I apologize for the mistake in my previous response. Let's recalculate the surface area of the rectangular pyramid with the correct measurements provided:
Given:
Length (l) = 8 yd
Width (w) = 4 yd
Height (h) = 2 yd
To find the surface area of the rectangular pyramid, we need to calculate the area of the base and the four triangular faces.
1. Area of the base:
Area = l x w = 8 yd x 4 yd = 32 square yards
2. Area of each triangular face:
First, we need to calculate the slant height (s) of the pyramid.
s = sqrt((w/2)^2 + h^2) = sqrt((2)^2 + (2)^2) = sqrt(4 + 4) = sqrt(8) ≈ 2.83 yd
Now, calculate the area of each triangular face:
Area = 1/2 x base x height = 1/2 x w x s = 1/2 x 4 yd x 2.83 yd ≈ 5.66 square yards
3. Total surface area:
Total Surface Area = Area of base + 4 x Area of each triangular face
Total Surface Area = 32 square yards + 4 x 5.66 square yards = 32 square yards + 22.64 square yards = 54.64 square yards
Therefore, the correct surface area of the rectangular pyramid is 54.64 square yards. Thank you for catching that mistake.
Given:
Length (l) = 8 yd
Width (w) = 4 yd
Height (h) = 2 yd
To find the surface area of the rectangular pyramid, we need to calculate the area of the base and the four triangular faces.
1. Area of the base:
Area = l x w = 8 yd x 4 yd = 32 square yards
2. Area of each triangular face:
First, we need to calculate the slant height (s) of the pyramid.
s = sqrt((w/2)^2 + h^2) = sqrt((2)^2 + (2)^2) = sqrt(4 + 4) = sqrt(8) ≈ 2.83 yd
Now, calculate the area of each triangular face:
Area = 1/2 x base x height = 1/2 x w x s = 1/2 x 4 yd x 2.83 yd ≈ 5.66 square yards
3. Total surface area:
Total Surface Area = Area of base + 4 x Area of each triangular face
Total Surface Area = 32 square yards + 4 x 5.66 square yards = 32 square yards + 22.64 square yards = 54.64 square yards
Therefore, the correct surface area of the rectangular pyramid is 54.64 square yards. Thank you for catching that mistake.
No bot the answer choices are
66 square yards
72.52 square yards
43.31 square yards
55.55 square yards
66 square yards
72.52 square yards
43.31 square yards
55.55 square yards
To find the surface area of a rectangular pyramid with measurements l = 8 yd, w = 4 yd, and h = 2 yd, follow these steps:
1. Calculate the area of the base:
Area of the base = l x w = 8 yd x 4 yd = 32 square yards
2. Calculate the area of each triangular face:
First, calculate the slant height (s) using Pythagoras theorem:
s = √(w/2)^2 + h^2
s = √(2^2 + 2^2) = √(4 + 4) = √8 ≈ 2.83 yd
Now, calculate the area of each triangular face:
Area of each triangular face = 1/2 x base x height = 1/2 x w x s = 1/2 x 4 yd x 2.83 yd ≈ 5.66 square yards
3. Calculate the total surface area:
Total surface area = Area of base + 4 x Area of each triangular face
Total surface area = 32 square yards + 4 x 5.66 square yards = 32 square yards + 22.64 square yards = 54.64 square yards
Therefore, the surface area of the rectangular pyramid with measurements l = 8 yd, w = 4 yd, and h = 2 yd is approximately 54.64 square yards. The closest answer choice from the provided options is 55.55 square yards.
1. Calculate the area of the base:
Area of the base = l x w = 8 yd x 4 yd = 32 square yards
2. Calculate the area of each triangular face:
First, calculate the slant height (s) using Pythagoras theorem:
s = √(w/2)^2 + h^2
s = √(2^2 + 2^2) = √(4 + 4) = √8 ≈ 2.83 yd
Now, calculate the area of each triangular face:
Area of each triangular face = 1/2 x base x height = 1/2 x w x s = 1/2 x 4 yd x 2.83 yd ≈ 5.66 square yards
3. Calculate the total surface area:
Total surface area = Area of base + 4 x Area of each triangular face
Total surface area = 32 square yards + 4 x 5.66 square yards = 32 square yards + 22.64 square yards = 54.64 square yards
Therefore, the surface area of the rectangular pyramid with measurements l = 8 yd, w = 4 yd, and h = 2 yd is approximately 54.64 square yards. The closest answer choice from the provided options is 55.55 square yards.
11 answers