can prisms that have the same height and same base perimeter have different volumes?
No
Why not?
http://www.math.com/tables/geometry/volumes.htm
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
Just checked by first calculation, should have been
72√3/2 or appr 62.4
My conclusion remains the same
Yes, prisms that have the same height and the same base perimeter can have different volumes.
To understand why, let's start by reviewing the equation for the volume of a prism. The volume of a prism is given by the formula V = Bh, where B represents the base area and h represents the height.
Now, let's consider two prisms with the same height and the same base perimeter. The base perimeter is the sum of all the lengths of the sides of the base of the prism.
While the base perimeter of the two prisms is the same, we can have different shapes for the base of each prism. For example, we can have a rectangular prism with a base length of 4 units and a base width of 2 units, which results in a base perimeter of 4 + 4 + 2 + 2 = 12 units. The volume of this prism would be V1 = (4 * 2) * h = 8h units^3.
On the other hand, we can have a square prism with a base side length of 3 units, which also gives a base perimeter of 3 + 3 + 3 + 3 = 12 units. The volume of this prism would be V2 = (3 * 3) * h = 9h units^3.
As you can see, even though the height and the base perimeter are the same for both prisms, the volumes V1 and V2 are different. Therefore, prisms with the same height and the same base perimeter can have different volumes due to variations in their base shapes.