How to Find the Surface Area of 3D Shapes

Hi, and welcome this video lesson on the surface area of 3D objects.

A lot of times math problems can intimidate us with pictures or diagrams—but don’t worry—they break down the steps very nicely, so let me go ahead and walk you through one.

Right, so what do we know? Well, we know that we need the surface area of this 3D object, and that the surface area of 3D objects, especially when they look like this—a box—it’s the sum of the area of its 6 sides. In our problem we know that we have a height of 4, a width of 20, and a length of 32.

We have a total of 6 sides, so let’s figure out what those areas will be.

To find the area of the ends, we just have to multiply the width times the height, and since there are 2 ends, we can go ahead and multiply that resulting number by 2, like this.

Now to find the short sides we multiply height times length, and then since there are 2 of them, we multiply that by 2. Now for our big sides, length times width, and there are also 2 of those, so let’s go ahead and multiply that by 2 as well.

Or, more simply: height times width, times 2; height times length, times 2; length times width, times 2. For the ends we get 80 square units, but there are 2 ends, so we multiply that by 2, 160.

For the short sides we get an area of 128 but multiply that by 2 and we end up with 256. Finally, for our big sides we have an area of 32 times 20, which is 640, multiplied by 2, equals 1280 square units. We add those areas together in order to get a total surface area, so 160 plus 256, plus 1280, is equal to a total of 1,696, that is our surface area.

I hope that helps! Thanks so much for watching this video lesson, and until next time, happy studying!