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)
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=5.36cm⟹Base 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