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Area and perimeter of a regular pentagon

pentagon

pentagon C c R r 108° 36° A B C D E a a a a a O
aedge
Ccircumcircle
cincircle
Rradius (circumcircle)
rradius (incircle)
Ocenter

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edge

a =

circumcircle (radius)

R =

incircle (radius)

r =

area

A =

perimeter

P =

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Calculation procedure

Formulas

pentagon

area
$$ A = \frac{\sqrt{25 + 10 \cdot \sqrt{5}}}{4} a^2 $$
perimeter
$$ P = 5 \cdot a $$
circumcircle (radius)
$$ R = \frac{\sqrt{50 + 10 \cdot \sqrt{5}}}{10} a $$
incircle (radius)
$$ r = \frac{\sqrt{25 + 10 \cdot \sqrt{5}}}{10} a $$

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