Pentadecagon

Calculate the content of a regular 15-sides polygon inscribed in a circle with radius r = 4. Express the result to two decimal places.

Correct result:

S =  48.8084

Solution:

n=15 r=4  α=2π2⋅ n=2⋅ 3.14162⋅ 15≐0.2094  sin⁡α=a/2:r  a=2⋅ r⋅ sin⁡(α)=2⋅ 4⋅ sin⁡(0.2094)≐1.6633 cos⁡α=h:r  h=r⋅ cos⁡(α)=4⋅ cos⁡(0.2094)≐3.9126  S1=a⋅ h2=1.6633⋅ 3.91262≐3.2539  S=n⋅ S1=15⋅ 3.2539=48.8084

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