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 150.2094  sinα=a/2:r  a=2 r sin(α)=2 4 sin(0.2094)1.6633 cosα=h:r  h=r cos(α)=4 cos(0.2094)3.9126  S1=a h2=1.6633 3.912623.2539  S=n S1=15 3.2539=48.8084



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