# Regular 5-gon

Calculate area of the regular pentagon with side 7 cm.

Result

S =  84.3 cm2

#### Solution:

$v = \dfrac{ 7 }{2} cotg (\dfrac{360}{10}) \ \\ S_1 = \dfrac12 7 \cdot v \ \\ S = 5 S_1 = \dfrac{ 5}{ 4} 7^2 cotg( 36 ^\circ ) = 84.3 \ \text{cm}^2$

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