Nonagon

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:

$$\begin{gathered} r=10\text{ cm } \\ n=9 \\ A=360\mathrm{/}n=360\mathrm{/}9=40\text{ ° } \\ \tan A\mathrm{/}2={\displaystyle \frac{a\mathrm{/}2}{r}} \\ a=2\cdot r\cdot \tan (A\mathrm{/}2)=2\cdot 10\cdot \tan (40\mathrm{/}2)\doteq 7.2794\text{ cm } \\ {S}_1={\displaystyle \frac{r\cdot a}{2}}={\displaystyle \frac{10\cdot 7.2794}{2}}\doteq 36.397{\text{cm}}^2 \\ S=n\cdot S_1=9\cdot 36.397=327.5732{\text{cm}}^2 \end{gathered}$$

$o=n\cdot a=9\cdot 7.2794=65.5146\text{ cm}$

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Showing 2 comments:

Math student

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

1 year ago  Like

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)

1 year ago  Like

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