# Pentagon

Calculate the area of regular pentagon, which diagonal is u=17.

Result

S =  325.43

#### Solution:

$u = 17 \ \\ A = (180-360/5)/2 = 54 \ ^\circ \ \\ B = 360/5/2 = 36 \ ^\circ \ \\ \ \\ a = u \cdot \ \sin(A) = 17 \cdot \ \sin(54^\circ ) \doteq 13.7533 \ \\ h = a/2 /\tan (B) = 13.7533/2 /\tan (36^\circ ) \doteq 9.4649 \ \\ \ \\ S_{ 1 } = \dfrac{ a \cdot \ h }{ 2 } = \dfrac{ 13.7533 \cdot \ 9.4649 }{ 2 } \doteq 65.0867 \ \\ S = 5 \cdot \ S_{ 1 } = 5 \cdot \ 65.0867 \doteq 325.4334 = 325.43$

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