Pentagon

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

Correct result:

S =  325.43

Solution:

u=17 A=(180−360/5)/2=54∘ B=360/5/2=36∘  a=u⋅ sin⁡(A)=17⋅ sin⁡(54∘)≐13.7533 h=a/2/tan⁡(B)=13.7533/2/tan⁡(36∘)≐9.4649  S1=a⋅ h2=13.7533⋅ 9.46492≐65.0867 S=5⋅ S1=5⋅ 65.0867=325.43

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