# Surface Area & Volume of an Octahedron

Instructor: Mark Boster
If you had an octahedron and needed to find the surface area or the volume of said octahedron, there are formulas to help you. It isn't hard at all if you just follow the directions.

## Octopus!

Sharon was at the beach one day when she saw an object lying in the sand. She went up to it, looked at it, and counted the legs. There were eight of them, so she knew it was an octopus because Octo means eight.

## Octahedron

An octahedron is a space figure that has eight sides. Get it...OCTApus OCTAhedron. Today, let's focus on a regular octahedron. A regular octahedron has an equilateral triangle for each of its eight sides. Or if you prefer, it has two pyramids hooked together at the base. ## Surface Area

So let's say you want to lay carpet on your octahedron. We would need to find the surface area. There is a formula for that. It is pretty easy. The area of an octahedron is 2 multiplied by the length of an edge squared multiplied by the square root of three. Let's try it for an octahedron with an edge of ten inches. Use a calculator if you have one. Here we go.

First, enter 2 in your calculator

Second, since the edge is 10 you square it and get 100 . Multiply the 2 by 100

Multiply that by the square root of 3.

If you did all that correctly, you should have a surface area of 346.41 sq in.

### Understand it.

Let's try it with a regular octahedron with an edge of 5.

First, enter 2 into your calculator.

Second multiply 2 by the 25 (that is 5 squared)

Now, multiply that by the square root of 3.

86.6 sq inches. ## Volume of a Regular Octahedron.

To find the volume of a regular octahedron, find the edge. You are going to need this.

Now just follow the formula in order.

Let's say the edge is 10 again.

First, cube 10.

10 x 10 x 10 = 1,000

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