Find the surface area of a rectangle 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

The surface area of a rectangular pyramid can be found using the formula:

Surface Area = l*w + l * sqrt((w/2)^2 + h^2) + w * sqrt((l/2)^2 + h^2)

Given:
l = 8 cm
w = 4 cm
h = 2 cm

Plugging in these values into the formula, we have:

Surface Area = 8*4 + 8 * sqrt((4/2)^2 + 2^2) + 4 * sqrt((8/2)^2 + 2^2)

Simplifying,

Surface Area = 32 + 8 * sqrt((2)^2 + 4) + 4 * sqrt((4)^2 + 4)

Surface Area = 32 + 8 * sqrt(4 + 4) + 4 * sqrt(16 + 4)

Surface Area = 32 + 8 * sqrt(8) + 4 * sqrt(20)

Surface Area ≈ 32 + 8 * 2.83 + 4 * 4.47

Surface Area ≈ 32 + 22.64 + 17.88

Surface Area ≈ 72.52

Therefore, the surface area of the rectangular pyramid is approximately 72.52 square centimeters.