First, let's find the area of the base of the pyramid. The base is a rectangle, so we can use the formula for the area of a rectangle: area = length * width.
area of base = 8 cm * 4 cm = 32 cm²
Next, let's find the lateral area of the pyramid. The lateral area represents the combined area of the four triangular faces of the pyramid. Each triangular face has base length equal to the width of the rectangle and height equal to the height of the pyramid.
lateral area = 4 * (1/2 * 4 cm * 2 cm) = 4 * (4 cm²) = 16 cm²
Finally, let's find the total surface area of the pyramid. The total surface area is the sum of the area of the base and the lateral area.
total surface area = area of base + lateral area = 32 cm² + 16 cm² = 48 cm²
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is 48 cm².
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) Do the problem in parts
3 answers
Incorrect, do the problem with the formula for surface area in parts
Apologies for the previous incorrect response. Let's calculate the surface area of the rectangular pyramid in parts.
First, let's calculate the area of the base of the pyramid. The base is a rectangle with length (l) of 8 cm and width (w) of 4 cm.
Area of the base = length * width
= 8 cm * 4 cm
= 32 cm²
Next, let's calculate the area of each triangular face of the pyramid. The rectangular pyramid has four triangular faces.
Area of one triangular face = (1/2) * base * height
= (1/2) * 4 cm * 2 cm
= 4 cm²
Since the pyramid has four triangular faces, the total area of the triangular faces would be:
Total area of the triangular faces = 4 * 4 cm²
= 16 cm²
Finally, let's calculate the total surface area of the pyramid. The total surface area is the sum of the area of the base and the area of the triangular faces.
Total surface area = Area of the base + Total area of the triangular faces
= 32 cm² + 16 cm²
= 48 cm²
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is 48 cm².
First, let's calculate the area of the base of the pyramid. The base is a rectangle with length (l) of 8 cm and width (w) of 4 cm.
Area of the base = length * width
= 8 cm * 4 cm
= 32 cm²
Next, let's calculate the area of each triangular face of the pyramid. The rectangular pyramid has four triangular faces.
Area of one triangular face = (1/2) * base * height
= (1/2) * 4 cm * 2 cm
= 4 cm²
Since the pyramid has four triangular faces, the total area of the triangular faces would be:
Total area of the triangular faces = 4 * 4 cm²
= 16 cm²
Finally, let's calculate the total surface area of the pyramid. The total surface area is the sum of the area of the base and the area of the triangular faces.
Total surface area = Area of the base + Total area of the triangular faces
= 32 cm² + 16 cm²
= 48 cm²
Rounded to the nearest hundredth, the surface area of the rectangular pyramid is 48 cm².