Question

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.

Answer 1

[AI-generated answer — Bot GPT 3.5]

A rectangular pyramid has a rectangular base and four triangular faces.

The formula to find the surface area of a rectangular pyramid is:
Surface Area = Base Area + (1/2 * Perimeter * Slant Height)

First, let's find the base area:
Base Area = length * width
Base Area = 8 cm * 4 cm
Base Area = 32 cm^2

Next, let's find the perimeter of the base:
Perimeter = 2 * (length + width)
Perimeter = 2 * (8 cm + 4 cm)
Perimeter = 2 * 12 cm
Perimeter = 24 cm

Now, let's find the slant height:
Using the Pythagorean theorem, we can find the slant height as the hypotenuse of a right triangle where the height is one leg and half of the base length is the other leg.
Slant Height = sqrt(height^2 + (base length / 2)^2)
Slant Height = sqrt(2 cm^2 + (4 cm / 2)^2)
Slant Height = sqrt(2 cm^2 + 2 cm^2)
Slant Height = sqrt(4 cm^2)
Slant Height = 2 cm

Now, let's calculate the surface area:
Surface Area = Base Area + (1/2 * Perimeter * Slant Height)
Surface Area = 32 cm^2 + (1/2 * 24 cm * 2 cm)
Surface Area = 32 cm^2 + 24 cm^2
Surface Area = 56 cm^2

The surface area of the rectangular pyramid is 56 cm^2.