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 cm2
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 = 8 cm and width w = 4 cm. The area of the base is therefore A = l * w = 8 cm * 4 cm = 32 cm^2.
There are 4 triangular faces on a rectangular pyramid. The area of each triangular face can be found using the formula: A = (1/2) * base * height.
For the first triangular face, the base is the same as the length of the base of the pyramid, which is 8 cm, and the height is equal to the height of the pyramid, which is 2 cm. Therefore, the area of the first triangular face is A1 = (1/2) * 8 cm * 2 cm = 8 cm^2.
The second and third triangular faces have the same measurements, so their areas are also the same. The base of each face is equal to the width of the base of the pyramid, which is 4 cm, and the height is still 2 cm. Therefore, the area of each of the second and third triangular faces is A2 = A3 = (1/2) * 4 cm * 2 cm = 4 cm^2.
Finally, the fourth triangular face also has the same measurements, so its area is also 4 cm^2.
Now we can add up the areas of all the faces:
Surface area = Area of base + Area of first triangular face + Area of second triangular face + Area of third triangular face + Area of fourth triangular face
Surface area = 32 cm^2 + 8 cm^2 + 4 cm^2 + 4 cm^2 + 4 cm^2
Surface area = 52 cm^2.
Therefore, the surface area of the rectangular pyramid is 52 cm^2, rounded to the nearest hundredth cm^2.
wrong 52 is not the answer
Apologies for the incorrect calculation.
The surface area of a rectangular pyramid can be found by calculating the area of the base rectangle and the area of the four triangular faces.
The area of the base rectangle can be calculated as A = l * w = 8 cm * 4 cm = 32 cm^2.
To find the area of each triangular face, we need to calculate the area of the base of the triangle and multiply it by the height of the pyramid.
The base of the triangle is equal to the length or width of the base rectangle. So, the first triangular face has a base of 8 cm and height of 2 cm. The area of this face is A1 = (1/2) * 8 cm * 2 cm = 8 cm^2.
Similarly, the second, third, and fourth triangular faces also have areas of 8 cm^2 each.
Now, we can calculate the total surface area:
Surface area = Area of base + Area of first triangular face + Area of second triangular face + Area of third triangular face + Area of fourth triangular face
Surface area = 32 cm^2 + 8 cm^2 + 8 cm^2 + 8 cm^2 + 8 cm^2
Surface area = 64 cm^2.
Therefore, the surface area of the rectangular pyramid is 64 cm^2, rounded to the nearest hundredth cm^2.