Area and perimeter of a regular pentagon

Name: Area and perimeter of a regular pentagon
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a =

R =

r =

A =

P =

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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)

$$ r = \frac{\sqrt{25 + 10 \cdot \sqrt{5}}}{10} a $$