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 \frac{bh}{2}

The area of each can be gotten from \frac{\overbrace{rsin(22.5)}^{\text{b}}\overbrace{ rcos(22.5)}^{\text{h}}}{2}

There are 16 such triangles, so we have

So, the area of the octagon is 8r^{2}sin(22.5)cos(22.5)=2\sqrt{2}r^{2}

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 :

Area = \sqrt{2} r^2

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 8r^{2}cos(22.5)(sin(22.5)=2\sqrt{2}r^{2}

If we use the 8 isosceles triangles each with area \frac{1}{2}r^{2}sin(45), we get 4r^{2}sin(45)=2\sqrt{2}r^{2}

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.