What is the surface area of a rectangular pyramid with the measurements l = 13cm, w = 11cm, and h = 8cm? Express your answer as a decimal rounded to the nearest hundredth.

Answer 1

The surface area of a rectangular pyramid is given by the formula:

Surface Area = lw + lh + wh + (1/2)pl

where l is the length of the base, w is the width of the base, h is the height of the pyramid, and p is the slant height.

Given l = 13 cm, w = 11 cm, and h = 8 cm, we need to find the slant height p.

The slant height can be found using the Pythagorean Theorem, where p is the hypotenuse of a right triangle with legs of length l/2 and h.

Using the Pythagorean Theorem, we have:

p^2 = (l/2)^2 + h^2

p^2 = (13/2)^2 + 8^2
p^2 = 169/4 + 64
p^2 = 169/4 + 256/4
p^2 = 425/4

Taking the square root of both sides gives:

p = sqrt(425/4) = sqrt(425)/2

Now we can calculate the surface area:

Surface Area = lw + lh + wh + (1/2)pl
Surface Area = 13*11 + 13*8 + 11*8 + (1/2) * sqrt(425)/2 * 13
Surface Area = 143 + 104 + 88 + sqrt(425)/4 * 13
Surface Area = 335 + 13sqrt(425)/4

Rounding to the nearest hundredth gives:

Surface Area ≈ 335 + 13sqrt(425)/4 ≈ 415.31 cm^2

Therefore, the surface area of the rectangular pyramid is approximately 415.31 cm^2.