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Rectangles A, B, and C represent bases of three prisms.
There are 4 different prisms that all have the same volume. Here is what the base of each prism looks like.
Four polygons on a grid. Polygon A, a 3 by 3 block with a 1 by 1 block missing from the corner. Polygon B, a right triangle 3 blocks by 4 blocks. Polygon C, a 4 by 4 rectangle with a 4 by 2 triangle missing from the top. Polygon D, 5 blocks arranged like a plus sign.
Any cross-section of a prism that is parallel to the base will be identical to the base. This means we can slice prisms up to help find their volume. For example, if we have a rectangular prism that is 3 units tall and has a base that is 4 units by 5 units, we can think of this as 3 layers, where each layer has cubic units. The volume of the figure is the number of cubic units that fill a three-dimensional region without any gaps or overlaps.
That means the volume of the original rectangular prism is , or 60, cubic units.
This works with any prism! If we have a prism with a height of 3 cm that has a base with an area of 20 cm2, then the volume is cm3 regardless of the shape of the base. In general, the volume of a prism with height and area is
For example, these two prisms both have a volume of 100 cm3.
Volume is the number of cubic units that fill a three-dimensional region with no gaps or overlaps.
This rectangular prism has 3 layers that are each 20 units3. So, the volume of the prism is 60 units3.