Calculate the area and perimeter of a regular nonagon if its radius of the inscribed circle is r = 10cm

Correct answer:

S =  327.5732 cm2
o =  65.5146 cm

Step-by-step explanation:

r=10 cm n=9  A=360/n=360/9=40   tan A/2 =  ra/2  a=2 r tan(A/2)=2 10 tan(40/2)7.2794 cm  S1=2r a=210 7.279436.397 cm2 S=n S1=9 36.397=327.5732 cm2
o=n a=9 7.2794=65.5146 cm

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Showing 3 comments:
Math student
I need to draw a nonagon for my daughter and she has to have each at 4cm

try to start with angle 360/9 = 40°... Draw nine isosceles triangles with base a=4 cm and opposite angle 40°.
Or if you may calculate diameter of described circle - draw a circle and divide it into nine equal segments. (divide by 40° angle)

Math student
Find the perimeter of a Regular Decagon whose one of the sibe is 27.9cm

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