Find the surface area of a rectangular pyramid with these measurements l = 13cm; w = 11cm and h = 8 cmExpress your answer as a decimal rounded to the nearest hundredth.

Answer 1

The surface area of a rectangular pyramid can be found by adding the area of the base to the areas of the four triangular faces.

The formula for the surface area of a rectangular pyramid is given by:
Surface Area = l*w + l*sqrt((w/2)^2 + h^2) + w*sqrt((l/2)^2 + h^2) + l*sqrt((w/2)^2 + h^2)

Substituting the given measurements, we have:
Surface Area = 13*11 + 13*sqrt((11/2)^2 + 8^2) + 11*sqrt((13/2)^2 + 8^2) + 13*sqrt((11/2)^2 + 8^2)

Calculating the terms inside the square roots:
(11/2)^2 + 8^2 = 121/4 + 64 = 585/4
(13/2)^2 + 8^2 = 169/4 + 64 = 601/4

Substituting these values back into the formula:
Surface Area = 143 + 13*sqrt(585/4) + 11*sqrt(601/4) + 13*sqrt(585/4)

Calculating the square roots:
sqrt(585/4) = 12.077
sqrt(601/4) = 12.221

Substituting these values back into the formula:
Surface Area = 143 + 13*12.077 + 11*12.221 + 13*12.077
Surface Area = 143 + 157.001 + 134.431 + 157.001
Surface Area = 591.433

Rounding to the nearest hundredth:
Surface Area ≈ 591.43

Therefore, the surface area of the rectangular pyramid is approximately 591.43 cm².