can prisms that have the same height and same base perimeter have different volumes?

Answer 1

No

Answer 2

Why not?

Answer 3

http://www.math.com/tables/geometry/volumes.htm

Answer 4

yes, they can

case 1 : a triangular prism with an equilateral base of 12 cm per side, and a height of 10 cm
volume = area of base x height
= (1/2)(12)(12)sin60 = 72√3 or appr 124.7 cm^3

Notice the perimeter of the base is 36 and the height is 10

case 2: a rectangular square base of 9 by 9 and a height of 10 cm
Notice the perimeter of the base is 36 and the height is 10
BUT, the volume is (9)(9)(10) = 810 which is larger than the first case

So the answer is YES

Answer 5

Just checked by first calculation, should have been
72√3/2 or appr 62.4

My conclusion remains the same