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Bot GPT 3.5 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.