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Volume of Prisms - Concept

Teacher/Instructor Brian McCall
Brian McCall

Univ. of Wisconsin
J.D. Univ. of Wisconsin Law school

Brian was a geometry teacher through the Teach for America program and started the geometry program at his school

We can calculate the volume of any prism simply by knowing the height of the prism and the area of one of its bases. When calculating prism volume, this volume formula can be applied to both right and oblique prisms with bases of any shape, such as triangles, quadrilaterals, or other polygons. A prism volume is a measurement of the space occupied by such solid.

If you want to calculate the volume of any prism, there is only two things that you need to know: One, what is the height of that prism, and two what is the area of one of your bases. So I'm going to shade in our bottom base here, and I'm going to label this as capital B. So when I write my volume formula, I'm going to say the volume, "V" of this prism, is equal to its base area times its capital H, its height. Where capital B is your base area and capital H is the height of the prism.
So the reason why this formula is useful is because you might have a triangular prism, a trapezoidal prism, a hexagonal prism. This formula will work no matter what kind of prism you have.
So whatever your base area is, and I guess I should write base area, you're going to substitute in that formula. So if this was a trapezoid, then you would substitute in B1 plus B2 times H, all divided by two. And that's how you would calculate your base area.
If you had, let's say, a regular hexagon, you're going to use apothem times side length times the number of sides, divided by two. So this way, this formula volume, equals base area times height, can be applied to any kind of prism.
One other thing, this is a right prism. If you had an oblique prism, as long as you know the height, and you can calculate its base area, that will be the same. You can use the same formula. It works for right prisms and oblique prisms.

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