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Video: Finding the Total Surface Area of a Rectangular Prism given Its Edge Lengths

Kathryn Kingham

Find the surface area of the rectangular prism shown.<Figure>

02:24

Video Transcript

Find the surface area of the rectangular prism shown here.

We can find the surface area of a rectangular prism with the formula shown here: two times the width times the length plus the length times the height plus the height times the width. Let’s break this formula down a little bit. Right now, I’ve just labelled the length, width, and height of our prism.

If we multiply the width times the length, which surface are we finding the area of? The one highlighted in green, it’s just the area of one of the bases. When we multiply the height times the length, you find the area of the bit shaded in yellow. The height multiplied by the width will give you the area of the part shaded in pink. And then we can distribute the two because each of these faces, the one shaded in green, pink, and yellow have an opposite that’s the same size as they are.

Now that we’ve talked a little bit about where the formula came from, let’s plug in the values and solve. Plug in all the values from the given prism. 29 times 39 is 1131. 30 times 39, 1170. 30 times 29 equals 870. Adding up those three sides equals 3171. And finally, multiplying that part by two equals 6342. We also have to add our units, which would be meters squared.

Each of these pieces, each of these faces represent an area. That’s why it’s going to be meters squared. Surface area is measured in units squared, which makes our final answer: 6342 meters squared.