Find the surface area of a rectangular pyramid with these measurements: l= 13 cm, w= 11 cm, and h = 8 cm. Express your answer as a decimal rounded to the nearest hundredth.(1 point for correct answer)
The surface area of a rectangular pyramid can be found using the formula:
SA = l * w + l * √(w/2)^2 + h^2 + w * √(l/2)^2 + h^2
Plugging in the values: l = 13 cm, w = 11 cm, h = 8 cm
SA = 13 * 11 + 13 * √(11/2)^2 + 8^2 + 11 * √(13/2)^2 + 8^2
SA = 143 + 13 * √(5.5)^2 + 64 + 11 * √(6.5)^2 + 64
SA = 143 + 13 * 2.34521 + 64 + 11 * 3.37485 + 64
SA = 143 + 30.48773 + 64 + 37.12335 + 64
SA = 143 + 30.48773 + 64 + 37.12335 + 64
SA = 338.61
Therefore, the surface area of the rectangular pyramid is 338.61 square centimeters.
wrong
I apologize for the error in my previous calculation. Let me correct it:
The surface area of a rectangular pyramid is given by the formula:
SA = l * w + 0.5 * l * √((w/2)^2 + h^2) + 0.5 * w * √((l/2)^2 + h^2)
Plugging in the values: l = 13 cm, w = 11 cm, h = 8 cm
SA = 13 * 11 + 0.5 * 13 * √((11/2)^2 + 8^2) + 0.5 * 11 * √((13/2)^2 + 8^2)
SA = 143 + 0.5 * 13 * √((5.5)^2 + 64) + 0.5 * 11 * √((6.5)^2 + 64)
SA = 143 + 0.5 * 13 * √(30.25 + 64) + 0.5 * 11 * √(42.25 + 64)
SA = 143 + 0.5 * 13 * √(94.25) + 0.5 * 11 * √(106.25)
SA = 143 + 0.5 * 13 * 9.70773 + 0.5 * 11 * 10.30688
SA = 143 + 63.17417 + 56.68784
SA = 263.86
Therefore, the surface area of the rectangular pyramid is 263.86 square centimeters, rounded to the nearest hundredth. Thank you for your patience.
wrong again
Let's correct the calculation:
The surface area of a rectangular pyramid is given by the formula:
SA = l * w + l * √((w/2)^2 + h^2) + w * √((l/2)^2 + h^2)
Given l = 13 cm, w = 11 cm, h = 8 cm
SA = 13 * 11 + 13 * √((11/2)^2 + 8^2) + 11 * √((13/2)^2 + 8^2)
SA = 143 + 13 * √(30.25 + 64) + 11 * √(42.25 + 64)
SA = 143 + 13 * √94.25 + 11 * √106.25
SA = 143 + 13 * 9.708 + 11 * 10.306
SA = 143 + 126.004 + 113.366
SA = 382.37
So, the surface area of the rectangular pyramid is 382.37 square centimeters, rounded to the nearest hundredth. Thank you for your patience.