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How To Calculate The Sides of a Octagon Using Windows Calculator

 

I will demonstrate graphically the steps needed to calculate the sides of a octagon using windows calculator with an example. It also demonstrates a practical use for Pythagorean Theorem. I decided to make this page because I was told that it's impossible to calculate the length of the sides of an octagon using only Pythagorean Theorem and simple math. Try it out.

Step 1

The end goal is to find the length of each side of a 48 inch octagon.

You can use whatever value you need for A and B. For a regular octagon A and B should be the same value.

Draw a square and divide it into two triangle.

First draw a square and divide it into two triangles. We need to find the length of the hypotenuse "C".

a2 + b2 = c2

To start the calculator

click Start | Run type calc click Ok

Switching to the Scientific Calculator

The calculator can be put into scientific mode.
click on View | Scientific

With Windows Calculator opened and in scientific mode type the following:

48  

squared button 

plus button 

48  

squared button

equals button

inverse check

squared button

67.8822509939085623424810587620655

Step 2

divide the hypotenuse "C" in half giving us a radius.

 

Now we need to divide the hypotenuse "C" in half giving us a radius.
Type in windows calculator the following:

67.8822509939085623424810587620655 divide button 2 equals button 33.9411254969542811712405293810328

Step 3

The Radius subtracted from the lenght of the side.

 

Now we subtract the radius 33.9411254969542811712405293810328 from the length of the square.
Type in windows calculator the following:
33.9411254969542811712405293810328 subtract button 48 equals button -14.0588745030457188287594706189672

 plus / minus button 14.05887450304571882875947061897 memory store button this answer gives us the length of this sides for a new triangle.

Step 4

we have another triangle where we want to find the hypotenuse "C" again.

Now we have another triangle where we want to find the hypotenuse "C" again. This answer will be the solution to the problem.

Type in windows calculator the following: MR so you don't have to re-enter #  
14.05887450304571882875947061897 squared button plus button memory read button 14.05887450304571882875947061897 squared button equals button
inverse check

squared button

19.8822509939085623424810587620694

  
Shows triangle at all four corners. Shows a b c sides of the triangle on the corners of the square. Shows square as octagon with a, b sides of corner triangle removed.


All 8 sides are 19.8822509939085623424810587620694 or 19 7/8+ in length.

Read More about Pythagorean Theorem

Octagon Layout Calculator For Large Framing Projects

Last Page Update

September 30, 2004

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