Dodecagon

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   sinA/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=n 425=12 6.25=75 cm2
o=n a=12 2.5882=31.0583 cm



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Most natural application of trigonometry and trigonometric functions is a calculation of the triangles. Common and less common calculations of different types of triangles offers our triangle calculator. Word trigonometry comes from Greek and literally means triangle calculation.

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