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Surface Area 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

Surface area is a two-dimensional property of a three-dimensional figure. Prisms have two congruent, parallel bases separated by lateral faces. Lateral faces are congruent rectangles with a height equal to the prism, unless oblique, and bases equal to the side lengths of the congruent bases. Therefore, to find the surface area of prisms, find the area of the bases and the lateral faces and sum them.

If you want to calculate the surface area of a prism, first you need to ask yourself well what is a prism? A prism is a 3 dimensional polyhedron of if we're going to use the plural we're going to say polyhedra which means more than 1 polyhedron with parallel congruent bases. So if we look at this diagram I've labeled the top and the bottom as my bases. And the sides as my lateral faces, these sides will make up what we call the lateral area. So if you want to calculate the surface area of this basically you could think of it as how much paint would I need to cover all the sides of this shape.
Well what I'm going to do is, I'm going to in my head break this apart into its parts so we're going to have a hexagon as its base and we're going to have 2 of them, so I guess I can calculate the area of this hexagon and then multiply it times 2 and then I'm going to have to ask myself well what do these lateral faces look like? It's pretty clear that they look like rectangles. Now if you have a regular hexagon as your base then you can assume that you're going to have 6 congruent rectangles. However if these are labeled as different lengths then you're going to have to calculate each one of these regular excuse me each one of these rectangles on their own. So the key to solving any problem that asks you for surface area, is to write your pieces separately, calculate their areas and then add them up.

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