Formula for calculating the voulume of an Octogon

An octagon has no volume. Though, It has area.

You can derive a general formula.

Let r equal the distance from the center to a vertex.

We can break it up into 16 right triangles by drawing another line from the center to the middle of a side and then find the area of each.

The angle of each triangle will be 22.5 degrees because 360/16=22.5.

The area of a triangle is

The area of each can be gotten from

There are 16 such triangles, so we have

So, the area of the octagon is

If you need volume, multiply by the depth as well.

Just enter your value of r and the depth, call it d, to find the volume.

For that matter, you could Google octagon volume and find many things. I just came up with this one.

Galactus? You sure? An octagon has eight sides i think? So, 8, triangles instead of 16?

Then, your final equation should be :



EDIT: Oh, i didn't check the numbers... sorry, i need to check more carefully next time.

I broke it up into 16 right triangles. Instead of the 8 isosceles. See what I mean?

Since there are 16 of these little right triangles, we have

If we use the 8 isosceles triangles each with area , we get

Same thing. I should've done that before. Easier. A good check though.

That's OK Unknown. I doubt if the poster responds back anyway.