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Prisms: Definition, Area & Volume Video

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  • 0:05 Prisms
  • 1:01 Measurements
  • 2:41 Surface Area
  • 4:24 The Volume
  • 5:16 Lesson Summary
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Lesson Transcript
Instructor: Yuanxin (Amy) Yang Alcocer

Amy has a master's degree in secondary education and has taught math at a public charter high school.

Watch this video lesson and you will see that there are different kinds of prisms. You will also learn how to separate a prism into its various parts so you can easily find the surface area. You will also learn the formula for the volume.

Prisms

A prism is a three-dimensional object with parallel straight sides and a top and bottom base that are the same polygonal shape. The base can be any shape as long as it is a polygon, meaning a two-dimensional shape with straight sides. We identify the various prisms by their bases. For example, if the base is a triangle, then we would call it a triangular prism. If the base is a square, then we would call it a square prism. Can you guess what we would call a prism with a pentagon as a base? That's right - we would call it a pentagonal prism. In real life, some skyscrapers are even the shape of prisms. Do you see how this skyscraper has parallel straight sides going up and how it has the same base at the top and bottom? This particular skyscraper has a rectangular base. Do you also see that if we took a cross-section anywhere along its length that the cross-section will always be the shape of the base?

Skyscraper prism with parallel sides
Skyscraper Prism

Measurements

Because the base plays a defining role in a prism, it is one of the important measurements we need in order to calculate our surface area and volume. The one measurement we need from the base part is the area it covers. We will label this measurement with a big B. So, remember, that when you see a big B, that it stands for the area of the base. If we had a square prism, then the area of our base would be the length times the width of the square. So, if our square was 4 inches by 4 inches, then our B would equal 16 inches squared, because the area of the base, which happens to be a square, is the length times the width of the square, so 4 * 4. If our prism had a triangular base, then we would need to calculate the area of a triangle if the problem didn't already give us the area. So, if our triangle was 4 inches across and 4 inches high, then our triangle is 4 * 4 / 2 = 8 inches squared.

The next important measurement that we need is the perimeter of the base. This we will label with a big P. To find the perimeter of the base, we would add up all the sides going around the base. For a square with sides that are 4 inches, our perimeter is 4 + 4 + 4 + 4 = 16 inches. If our prism is triangular with all the sides measuring 3 inches, then our perimeter is 3 + 3 + 3 = 9 inches.

The last measurement that we need is the height of the prism. So, if we had our prism standing on its base, the height is how tall the prism stands. This measurement will be labeled h.

Surface Area

Now that we have all our measurements in place, we can go ahead and use our formulas. The formula to find the surface area, the total area of just the surface, includes our area of the base, our perimeter, and our height.

Surface Area = 2 * B + P * h

What we are essentially doing is multiplying the area of the base by two because we have two bases and then we are adding that number to the surface area of just the sides of the prism which we find by multiplying the perimeter with the height.

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