Pentagon

Calculate the length of side, circumference and area of a regular pentagon, which is inscribed in a circle with radius r = 6 cm.

Correct result:

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

Solution:

r=6 a=2⋅ r⋅ sin⁡(π/5)=2⋅ 6⋅ sin⁡(3.1416/5)=7.0534 cm
o=5⋅ a=5⋅ 7.0534=35.2671 cm
h=r2−(a/2)2=62−(7.0534/2)2≐4.8541 S1=a⋅ h/2=7.0534⋅ 4.8541/2≐17.119 S=5⋅ S1=5⋅ 17.119=85.5951 cm2

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