Q:

Ryan and Scott are each studying a square pyramid.Which statement best describes the two pyramids? A.Both pyramids have the same total surface area, but the areas of the lateral faces and the areas of the bases are different in each pyramid.B.Both pyramids have the same total surface area, and the areas of the lateral faces and the areas of the bases are the same in each pyramid.C.Ryan’s pyramid has a greater surface area.D.Scott’s pyramid has a greater surface area.

Accepted Solution

A:
Surface Area = [Base Area] + 12 × Perimeter × [Slant Length]

Ryan square pyramid
[Base Area]=10*10=100 feet²
Perimeter=10+10+10+10=40 feet
[Slant Length]=12 feet
Surface Area=100+12*40*12=5860 feet²
Scott square pyramid  
[Base Area]=12*12=144 feet²
Perimeter=12+12+12+12=48 feet
[Slant Length]=10 feet
Surface Area=144+12*48*10=5904 feet²

the answer is D.Scott’s pyramid has a greater surface area.