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Question

The angle opposite to the base edge of a square pyramid on its lateral face is 30. If the slant height of the pyramid is 20cm, what is the lateral surface area of the pyramid? (Note that tan15=0.268)


A

4288cm2​​​

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B

428.8cm2​​​

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C

42.88cm2​​​

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D

600cm2​​​

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Solution

The correct option is B

428.8cm2​​​


Since the triangular face of a pyramid is isosceles, we have AC bisecting BD. Thus, using trigonometric ratios in ACD where CAD=BAD2=15, we have
tan15=CDAC=CD20
0.268=CD20
CD=0.268×20=5.36cmBase edge=2×5.36cm=10.72cm
Thus, Area of ACD=12×10.72×20=107.2cm2
Now, the lateral surface area of the pyramid = 4×Area of the ACD =4×107.2=428.8cm2​​​


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