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
To find the surface area of a rectangular pyramid, we need to find the area of each face and then add them together.
First, let's find the area of the base. The base of the pyramid is a rectangle with length l = 8 cm and width w = 4 cm. The area of a rectangle is found by multiplying its length and width, so the area of the base is:
Area of base = l * w = 8 cm * 4 cm = 32 cm^2
Next, let's find the area of the lateral faces. The lateral faces of a rectangular pyramid are triangles. To find the area of a triangle, we can use the formula:
Area of triangle = (1/2) * base * height
Considering the rectangular pyramid, the lateral faces have a base equal to the perimeter of the base rectangle, which is 2 * (l + w). The height of the lateral faces is h = 2 cm.
Area of each lateral face = (1/2) * base * height = (1/2) * (2 * (l + w)) * h
Substituting the values, we get:
Area of each lateral face = (1/2) * (2 * (8 cm + 4 cm)) * 2 cm = (1/2) * (2 * 12 cm) * 2 cm = 24 cm^2
Since a rectangular pyramid has four equal lateral faces, the total area of the lateral faces is:
Total area of lateral faces = 4 * 24 cm^2 = 96 cm^2
Finally, to find the surface area, we add the area of the base and the total area of the lateral faces:
Surface area = Area of base + Total area of lateral faces = 32 cm^2 + 96 cm^2 = 128 cm^2
Rounded to the nearest hundredth, the surface area of the rectangular pyramid with the given measurements is 128.00 cm^2.
To find the surface area of a rectangular pyramid, we need to find the area of each of its different faces.
First, let's calculate the area of the base, which is a rectangle. The formula for the area of a rectangle is length x width. In this case, the length (l) is 8 cm and the width (w) is 4 cm. So the area of the base is 8 cm x 4 cm = 32 cm^2.
Next, we need to calculate the areas of the four triangular faces. Each face is a right triangle, so we can use the formula for the area of a triangle, which is 1/2 x base x height.
The base of each triangle is equal to the width of the rectangle, which is 4 cm. The height of each triangle is equal to the height of the pyramid, which is 2 cm.
So the area of each triangular face is 1/2 x 4 cm x 2 cm = 4 cm^2.
Since there are four triangular faces, we need to multiply the area of one face by 4.
4 cm^2 x 4 = 16 cm^2.
Finally, we add the area of the base and the areas of the four triangular faces to get the total surface area of the pyramid.
32 cm^2 + 16 cm^2 = 48 cm^2.
Therefore, the surface area of the rectangular pyramid is 48 cm^2, rounded to the nearest hundredth.