Asked by Anonymous

can prisms that have the same height and same base perimeter have different volumes?
Answered by Anonymous
No
Answered by Anonymous
Why not?
Answered by Ms. Sue
http://www.math.com/tables/geometry/volumes.htm
Answered by Reiny
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
Answered by Reiny
Just checked by first calculation, should have been
72√3/2 or appr 62.4

My conclusion remains the same
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