Find the surface area of a rectangular pyramid with these measurements: l = 13 cm, w = 11 cm, and h = 8 cm

5 answers

To find the surface area of a rectangular pyramid, we need to find the area of each face and then add them together.

The base of the pyramid is a rectangle with length l = 13 cm and width w = 11 cm. The area of the base is l * w = 13 cm * 11 cm = 143 cm^2.

The other four faces are triangles. The height of the pyramid (h) is 8 cm, and the slant height of each triangular face can be found using the Pythagorean theorem:

slant height = √( (l/2)^2 + h^2 )

= √( (13/2)^2 + 8^2 )

= √( 6.5^2 + 64 )

= √( 42.25 + 64 )

= √106.25

≈ 10.31 cm

The area of each triangular face is given by A = (1/2) * base * height, where the base is the length of the rectangle, l, and the height is the slant height, ≈10.31 cm.

Each triangular face has an area of A = (1/2) * 13 cm * ≈10.31 cm = ≈66.96 cm^2.

So the total surface area of the rectangular pyramid is:

base area + 4 * triangular face area = 143 cm^2 + 4 * ≈66.96 cm^2 = 143 cm^2 + ≈267.85 cm^2 ≈ 410.85 cm^2.

Therefore, the surface area of the rectangular pyramid is approximately 410.85 cm^2.
its wrong keep trying bot!
Apologies for the incorrect response. Let's try again:

To find the surface area of a rectangular pyramid, we need to find the areas of all its faces and add them together.

The base of the pyramid is a rectangle with length l = 13 cm and width w = 11 cm. The area of the base is l * w = 13 cm * 11 cm = 143 cm^2.

Since the pyramid has four triangular faces, we need to find the area of each triangle.

To find the area of a triangle, we need the base and height. The base of each triangular face is equal to the length of the rectangle (l = 13 cm), and the height is equal to half the width of the rectangle (h = w/2 = 11 cm/2 = 5.5 cm).

The area of each triangular face is A = (1/2) * base * height = (1/2) * 13 cm * 5.5 cm = 35.75 cm^2.

Multiplying this area by 4 (as there are four triangular faces) gives us a total of 4 * 35.75 cm^2 = 143 cm^2.

Therefore, the surface area of the rectangular pyramid is the sum of the base area and the total area of the triangular faces:

Surface Area = base area + total area of triangular faces
= 143 cm^2 + 143 cm^2
= 286 cm^2.

Thus, the surface area of the rectangular pyramid is 286 cm^2.
Express your answer as a decimal rounded to the nearest hundredth.
Apologies for the oversight. Let's express the answer as a decimal rounded to the nearest hundredth.

The surface area of the rectangular pyramid is calculated to be 286 cm^2. Rounded to the nearest hundredth, the surface area is 286.00 cm^2.

Therefore, the surface area of the rectangular pyramid is approximately 286.00 cm^2.