# Nonagon

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

Result

S =  327.573 cm2
o =  65.515 cm

#### Solution:

$r=10 \ \text{cm} \ \\ n=9 \ \\ \ \\ A=360 / n=360 / 9=40 \ ^\circ \ \\ \ \\ \tan A/2=\dfrac{ a/2 }{ r } \ \\ \ \\ a=2 \cdot \ r \cdot \ \tan(A/2)=2 \cdot \ 10 \cdot \ \tan(40/2) \doteq 7.2794 \ \text{cm} \ \\ \ \\ S_{1}=\dfrac{ r \cdot \ a }{ 2 }=\dfrac{ 10 \cdot \ 7.2794 }{ 2 } \doteq 36.397 \ \text{cm}^2 \ \\ S=n \cdot \ S_{1}=9 \cdot \ 36.397 \doteq 327.5732 \doteq 327.573 \ \text{cm}^2$
$o=n \cdot \ a=9 \cdot \ 7.2794 \doteq 65.5146 \doteq 65.515 \ \text{cm}$

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Leave us a comment of this math problem and its solution (i.e. if it is still somewhat unclear...):

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

Matematik
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)

Tips to related online calculators
Pythagorean theorem is the base for the right triangle calculator.

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