Five-gon

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

Correct answer:

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

Step-by-step explanation:

n=5 R=6 cm  Φ=360/(2⋅ n)=360/(2⋅ 5)=36 ∘  sin Φ = 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)2​≐4.8541 cm  S1​=2a⋅ h​=27.0534⋅ 4.8541​≐17.119 cm2  S=n⋅ S1​=5⋅ 17.119=85.5951 cm2

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The Pythagorean theorem is the base for the right triangle calculator.
See also our trigonometric triangle calculator.

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