Expert: Scott A Wilson - 9/22/2009

Question
hey, thank you ahead of time for your help. I've been stuck on this problem:

a pyramid has a slant of 6 meters. if the base of the pyramid is a regular octagon with sides that measure 4 meters, find the lateral area of the pyramid.

I've come up with the answer 46m sq but its a multiple choice question and that answers not there. i believe I'm doing it right but i can't figure out how they've come up with their answer, can you please help?

thank you. Jennifer

Answer
The area of a pyramid is known to be Ah/3 where A is the area of the base and h is the height.

The area of the base is A = 2(1+√2)a² where a is the length of an edge.
For this octagon, the area of the base is 4²2(1+√2) = 32(1+√2).

The radius from the center of one side to the center of the other is 4(1+√2),
which is 9.656854249.

The radius from corner to corner is 4√(4 + 2√2), which is 8.789472908.

The slant of 6 meters would be the hypoteneuse to a right triangle that had one of these two as the base.

The center height would be √(6²-s²), where s is one of the two numbers given.

This would say that the volume would be 32(1+√2)√(6²-s²)/3.