A prism is a polyhedron, or solid figure that has congruent polygons as bases and has parallelograms (often rectangles) for lateral faces. Prisms are the same size and shape from bottom to top.

Want to know more about prisms?

Click on the image to open an applet to use for this investigation. The applet will open in a new browser tab or window.

Follow the exploration to determine the number of cubes it will take to fill a box that measures 5 units by 4 units by 3 units. (Typically, this is written in mathematical shorthand using the multiplication symbol, ×, which is read as "by" – so 5 × 4 × 3 is read, "5 by 4 by 3.")

In the sketch, the wide rod (second button, just beneath the cube) represents a row of cubes that is the width of the box. The deep rod (third button beneath the cube) represents a row of cubes that is the depth of the box.

Source: Cubes, NCTM Illuminations

Pause and Reflect

How does the product of the width and depth of a rectangular prism, or box, compare with the area of the base of the prism?

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Check Your Answer

The product of the width and depth is the same as the area of the base of the prism.

Use the interactive sketch to help you complete a table like the one shown below in your notes.

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Click here to check your table.

Width (units)	Depth (units)	Area of Base (square units)	Height of Prism (units)	Volume of Prism (cubic units)
5	4	20	3	(5x4)x3 = 60
5	4	20	4	(5x4)x4 = 80
5	4	20	5	(5x4)x5 = 100
5	4	20	6	(5x4)x6 = 120
5	4	20	h	(5x4)xh = 20h

Pause and Reflect

How can you express the volume of a prism in terms of the area of the base, B, and the height of the prism, h?

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Check Your Answer

The volume of a prism is equal to the area of the base, B, multiplied by the height of the prism, h: V = Bh