Five-gon

Calculate the side a, the circumference and the area of the regular 5-angle if Rop = 6cm.

Correct result:

a =  7.0534 cm
o =  35.2671 cm
S =  85.5951 cm2

Solution:

n=5 R=6 cm  Φ=360/(2 n)=360/(2 5)=36  sinΦ=a/2:R  a=2 R sinΦ=2 R sin36 =2 6 sin36 =2 6 0.587785=7.053=7.0534 cm
o=n a=5 7.0534=35.2671 cm
h=R2(a/2)2=62(7.0534/2)24.8541 cm  S1=a h2=7.0534 4.8541217.119 cm2  S=n S1=5 17.119=85.5951 cm2



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