How to calculate the distance from center to sides.

[squadjot]

Hi smart people.

Sorry, i might not even be able to formulate my question correct, so i made a sketch

I need to find the distance from the center of the shape, to the center of the sides. See JPG.

Known variable values are the width of the sides (in this example 100), and amount of sides.

So for an example, if i need to have 10 sides, what would the distance be? (green line)



[imgur URL removed] (if you cant see above pic)

Thanks


Edit: The green values on the sketch, are found simply by measuring

 

[tkhunny]

If they are REGULAR figures, also construct center-to-vertex and use your best triangle solution skills.

Note: It may help to know the name of such a thing, so you can look it up. "Apothem"

 

[yma16]

if you connect the center to a corner of the red side

Hi smart people.

Sorry, i might not even be able to formulate my question correct, so i made a sketch

I need to find the distance from the center of the shape, to the center of the sides. See JPG.

Known variable values are the width of the sides (in this example 100), and amount of sides.

So for an example, if i need to have 10 sides, what would the distance be? (green line)

the half of red, the green and the new line will form a triangle. Let a be the angle of the triangle at the center. Let the side be s and the green distance be d. Then s/2/d=tan(a).

Therefore d=s/2/tan(a), where a=(360/n)/2=180/n.

Let us say n=10, n is the number of sides and and s=100. d=100/2/tan(180/10)=50/tan(18) which is about 68.82.