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) Use the formula for surface area in parts
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = l * w + l * sqrt((w/2)^2 + h^2) + w * sqrt((l/2)^2 + h^2)
Plugging in the given measurements:
Surface Area = 8 * 4 + 8 * sqrt((4/2)^2 + 2^2) + 4 * sqrt((8/2)^2 + 2^2)
Simplifying:
Surface Area = 32 + 8 * sqrt((2)^2 + 4) + 4 * sqrt((4)^2 + 4)
Surface Area = 32 + 8 * sqrt(4 + 4) + 4 * sqrt(16 + 4)
Surface Area = 32 + 8 * sqrt(8) + 4 * sqrt(20)
Surface Area = 32 + 8 * 2.83 + 4 * 4.47
Surface Area = 32 + 22.64 + 17.88
Surface Area = 72.52
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is 72.52 cm².
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) Use the formula for surface area in parts
Incorrect, use the formula for surface area in a rectangular pyramid in parts
Apologies for the confusion. Let's use the surface area formula for a rectangular pyramid in parts.
The surface area of a rectangular pyramid can be calculated by finding the area of the base and the area of each triangular face.
The base of the pyramid is a rectangle, so the area of the base is given by:
Base Area = length * width
In this case, length (l) = 13 cm and width (w) = 11 cm.
Base Area = 13 cm * 11 cm = 143 cm²
Now, let's find the area of each triangular face.
The formula for the area of a triangle is given by:
Triangular Face Area = (1/2) * base * height
The rectangular pyramid has four triangular faces. Two of the triangular faces have a base equal to the length and a height equal to the height of the pyramid (h). The other two triangular faces have a base equal to the width and a height equal to the height of the pyramid (h).
Triangular Face 1 Area = (1/2) * length * height = (1/2) * 13 cm * 8 cm = 52 cm²
Triangular Face 2 Area = (1/2) * length * height = (1/2) * 13 cm * 8 cm = 52 cm²
Triangular Face 3 Area = (1/2) * width * height = (1/2) * 11 cm * 8 cm = 44 cm²
Triangular Face 4 Area = (1/2) * width * height = (1/2) * 11 cm * 8 cm = 44 cm²
Now, we can calculate the total surface area of the rectangular pyramid by summing the base area and the areas of the four triangular faces.
Surface Area = Base Area + Triangular Face 1 Area + Triangular Face 2 Area + Triangular Face 3 Area + Triangular Face 4 Area
Surface Area = 143 cm² + 52 cm² + 52 cm² + 44 cm² + 44 cm²
Surface Area = 335 cm²
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is 335.00 cm².
Incorrect try again
Apologies for the mistake. Let's try again using the correct formula for the surface area of a rectangular pyramid in parts.
The surface area of a rectangular pyramid can be calculated by finding the areas of the base, the lateral faces, and adding them together.
The area of the base, which is a rectangle, is given by:
Base Area = length * width
In this case, length (l) = 13 cm and width (w) = 11 cm.
Base Area = 13 cm * 11 cm = 143 cm²
Now, let's find the area of the lateral faces.
The lateral faces of the rectangular pyramid are four congruent triangles. The area of each triangular face can be calculated using the formula:
Triangular Face Area = (1/2) * base * height
The height of each triangular face is given by the height of the pyramid (h). The base of each triangular face is either the length (l) or the width (w).
Triangular Face 1 Area = (1/2) * length * height = (1/2) * 13 cm * 8 cm = 52 cm²
Triangular Face 2 Area = (1/2) * length * height = (1/2) * 13 cm * 8 cm = 52 cm²
Triangular Face 3 Area = (1/2) * width * height = (1/2) * 11 cm * 8 cm = 44 cm²
Triangular Face 4 Area = (1/2) * width * height = (1/2) * 11 cm * 8 cm = 44 cm²
Now, we can calculate the total surface area of the rectangular pyramid by summing the base area and the areas of the four triangular faces.
Surface Area = Base Area + Triangular Face 1 Area + Triangular Face 2 Area + Triangular Face 3 Area + Triangular Face 4 Area
Surface Area = 143 cm² + 52 cm² + 52 cm² + 44 cm² + 44 cm²
Surface Area = 335 cm²
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is 335.00 cm².
The surface area of a rectangular pyramid can be calculated using the formula:
Surface Area = l * w + l * sqrt((w/2)^2 + h^2) + w * sqrt((l/2)^2 + h^2)
Plugging in the given measurements:
Surface Area = 13 * 11 + 13 * sqrt((11/2)^2 + 8^2) + 11 * sqrt((13/2)^2 + 8^2)
Simplifying:
Surface Area = 143 + 13 * sqrt((5.5)^2 + 64) + 11 * sqrt((6.5)^2 + 64)
Surface Area = 143 + 13 * sqrt(30.25 + 64) + 11 * sqrt(42.25 + 64)
Surface Area = 143 + 13 * sqrt(94.25) + 11 * sqrt(106.25)
Surface Area = 143 + 13 * 9.71 + 11 * 10.3
Surface Area = 143 +126.23 + 113.3
Surface Area = 382.53
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is 382.53 cm².