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sadangryhow to solve a polygon

 Jun 1, 2016
 #1
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help fo polygon  sadcryingangryindecision

 Jun 1, 2016
 #2
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Let n be the number of sides of each polygon.

For angles...

Size of each angle = \(\frac{(n-2)(180)}{n}\)(in degrees)

 

For perimeters and areas(i love area questions :D)

Let n be the number of sides of each regular polygon and x be the length of each side

Perimeter = nx

 

Also I invented some of the area formulas to get the area of regular polygons(Length of each side = x)

(all trig functions in degrees)

Regular pentagon: \((x^2sin72)(1+cos36)\)

Remarks: The original regular pentagon area formula needs to know the apothem but my formula need not. 

Regular hexagon: \(3\sqrt{3}x^2\times\frac{1}{2}\)

Regular octagon: \((2x^2)(1+\sqrt2)\)

I found this all in one day. I used trigonometric functions when finding the regular pentagon and hexagon area formula and pythagoras theorem when finding the regular octagon area formula. Hope this can help you :D

 Jun 1, 2016

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