To find the surface area of a rectangular pyramid, you need to find the area of the base and the area of each triangular face, and then sum them up.
The base of the pyramid is a rectangle, so the area of the base is length x width:
Area of base = 8 yd. x 4 yd. = 32 yd^2
Next, we need to find the area of each triangular face. The triangular faces are all congruent, so we only need to find the area of one.
The height of the pyramid is given as 2 yd., which is also the slant height of the triangular face. The base of the triangle is the length of the rectangle, which is 8 yd.
To find the area of a triangle, you can use the formula:
Area of triangle = 0.5 x base x height
Area of triangle = 0.5 x 8 yd. x 2 yd. = 8 yd^2
Since there are 4 triangular faces, the total area of the triangular faces is 4 x 8 yd^2 = 32 yd^2.
Now, we can sum up the areas to find the total surface area of the pyramid:
Total surface area = Area of base + Area of triangular faces
Total surface area = 32 yd^2 + 32 yd^2 = 64 yd^2
Therefore, the surface area of the rectangular pyramid is 64 yd^2.
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
72.52 yd. 2
55.55 yd.2
55.55 yd. 2
43.31 yd.2
43.31 yd. 2
66 yd.2
66 yd. 2
4 answers
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Apologies for any confusion caused. Let's calculate the surface area of the rectangular pyramid using the given measurements.
The base of the pyramid is a rectangle, so the area of the base is length x width:
Area of base = 8 yd. x 4 yd. = 32 yd^2
Now, let's find the area of each triangular face. The height of the pyramid is given as 2 yd., which is also the slant height of the triangular face. The base of the triangle is the width of the rectangle, which is 4 yd.
To find the area of a triangle, you can use the formula:
Area of triangle = 0.5 x base x height
Area of triangle = 0.5 x 4 yd. x 2 yd. = 4 yd^2
Since there are 4 triangular faces, the total area of the triangular faces is 4 x 4 yd^2 = 16 yd^2.
Now, we can sum up the areas to find the total surface area of the pyramid:
Total surface area = Area of base + Area of triangular faces
Total surface area = 32 yd^2 + 16 yd^2 = 48 yd^2
Therefore, the surface area of the rectangular pyramid with the given measurements is 48 yd^2.
The base of the pyramid is a rectangle, so the area of the base is length x width:
Area of base = 8 yd. x 4 yd. = 32 yd^2
Now, let's find the area of each triangular face. The height of the pyramid is given as 2 yd., which is also the slant height of the triangular face. The base of the triangle is the width of the rectangle, which is 4 yd.
To find the area of a triangle, you can use the formula:
Area of triangle = 0.5 x base x height
Area of triangle = 0.5 x 4 yd. x 2 yd. = 4 yd^2
Since there are 4 triangular faces, the total area of the triangular faces is 4 x 4 yd^2 = 16 yd^2.
Now, we can sum up the areas to find the total surface area of the pyramid:
Total surface area = Area of base + Area of triangular faces
Total surface area = 32 yd^2 + 16 yd^2 = 48 yd^2
Therefore, the surface area of the rectangular pyramid with the given measurements is 48 yd^2.
The answer is 72.52