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 ∘  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)2​≐4.8296 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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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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