Find the area of a regular dodecagon (n=12) if the radius of the circumscribed circle is 5 cm.

Correct answer:

S =  75 cm2
o =  31.0583 cm

Step-by-step explanation:

R=5 cm n=12  A=360/n=360/12=30   sin A/2 =  Ra/2  a=2 R sin(A/2)=2 5 sin(30/2)2.5882 cm  r=R2(a/2)2=52(2.5882/2)24.8296 cm  S1=2r a=24.8296 2.5882=425=6.25 cm2 S=n S1=12 425=412 25=4300=75 cm2
o=n a=12 2.5882=31.0583 cm

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