masterartill Posts: 1, Reputation: 1 New Member #1 Apr 25, 2007, 07:27 PM
Area and volume of an octagon
How do you find the area of a octagon
How do you find the area of a hexagonal prism's surface area
How do your find the volume of a octagonal prism
 ebaines Posts: 12,132, Reputation: 1307 Expert #2 Apr 26, 2007, 05:29 AM
Originally Posted by masterartill
how do you find the area of a octagon
how do you find the area of a hexagonal prism's surface area
how do your find the volume of a octagonal prism
Think of an octagon as basically a square with 4 triangles cut out of the corners. The area is therefore the area of the square minus the areas of the 4 corner triangles. The only hard part is figuring the lengths of the legs of the triangles.

Surface area of a prism would be the area of the top + area of the bottom + area of all the sides. So you need to be able to calculate the area of the hexagon son the top and bottom, which you can do by adding the areas of triangles and/or rectangles that can be put together to make up the hexagon. The side walls are simply rectangles, so finding their area is easy.

Volume of a regular prism is base area times height, regardless of the shape (octagonal, hexagonal, square, etc).
 vrooje Posts: 28, Reputation: 2 New Member #3 Apr 26, 2007, 03:08 PM
Just to add to what ebaines said:

Finding the area of a polygon is not always difficult. If it's a regular polygon, it's often very simple. I believe much of ebaines' answer assumes you're talking about regular polygons and right prisms.

One way to find the area of any regular polygon is $A = \frac{1}{2}ap$ where $a$ is the apothem and $p$ is the perimeter of the figure.

Another way is the divide-and-conquer method, i.e. breaking up the polygon into a series of smaller polygons (usually triangles and rectangles) for which you can determine the area. This works even if the polygon is not regular.
 spotdart Posts: 1, Reputation: 1 New Member #4 May 17, 2007, 06:55 PM
I did some work on this type of problem and found a useful formula to determine the are of a regular polygon. It is as follow:

tan(90-180/S).25L^2S

where S is the number of sides, and L is the length of one of those sides.
 ebaines Posts: 12,132, Reputation: 1307 Expert #5 May 18, 2007, 05:51 AM
spotdart - you're right, but this is the same formula as the one provided by vrooje, given that for a regular polygon the apothem is equal to (L/2)*tan(90-180/s).
 willcurt Posts: 1, Reputation: 1 New Member #6 Jan 8, 2008, 07:26 PM
How do you find the volume of a octigon prisum
 djross Posts: 1, Reputation: 1 New Member #7 Nov 17, 2010, 08:29 AM
Area of an Octagon Box
If you happen to know the length of a regular side of an octagon box, meaning all the sides are of the same length, then you can quite easily find the area of the octagon. This is also part of the volume of an octagon box calculation.
Here's what you do. Take the length of one side in inches, any side, square it, then multiply by 4.8284. The result will be area in square inches of this regular octagon figure.
A = s squared times 4.8284
Then if you want to find the volume of this octagon box, multiply the area of the octagon times the depth to find the volume.

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