Question
Find a 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
Answers
Answered by
GPT 3.5
To compute the surface area of a rectangular pyramid, we need to add the area of the base to the areas of the four congruent triangular faces.
The area of the base is given by the formula: A_base = l * w
Substituting the given measurements: A_base = 8 cm * 4 cm = 32 cm^2
The area of each triangular face is given by the formula: A_triangle = 0.5 * base * height
Substituting the given measurements: A_triangle = 0.5 * 8 cm * 2 cm = 8 cm^2
Since there are four triangular faces, the total area of the triangular faces is: 4 * 8 cm^2 = 32 cm^2
Finally, we compute the total surface area by adding the area of the base and the area of the triangular faces: Total surface area = A_base + Total triangular area = 32 cm^2 + 32 cm^2 = 64 cm^2.
Rounding to the nearest hundredth, the surface area of the pyramid is 64.00 cm^2.
The area of the base is given by the formula: A_base = l * w
Substituting the given measurements: A_base = 8 cm * 4 cm = 32 cm^2
The area of each triangular face is given by the formula: A_triangle = 0.5 * base * height
Substituting the given measurements: A_triangle = 0.5 * 8 cm * 2 cm = 8 cm^2
Since there are four triangular faces, the total area of the triangular faces is: 4 * 8 cm^2 = 32 cm^2
Finally, we compute the total surface area by adding the area of the base and the area of the triangular faces: Total surface area = A_base + Total triangular area = 32 cm^2 + 32 cm^2 = 64 cm^2.
Rounding to the nearest hundredth, the surface area of the pyramid is 64.00 cm^2.