Answer :

caylus
Hello,

The nonagon, polygon with 9 sides, can be divided in 9 triangles which area is
a*c/2
a is the apothem et c the side
Center's angle is 360°/9=40°

as a/14=cos 20°, and (c/2)/14=sin 20°

a*c/2=14*14*sin 20°*cos 20°=14*7*sin40°=98*sin 40°=62,993185...
Area of the nonagon is 9*98*sin 40°=882*sin 40°=566,93867... (in²)

The area of a regular nonagon is [tex]567 \ in^{2}[/tex].

To understand the calculations, check below

Nonagon:

A nonagon contains 9 straight sides and 9 vertices connecting these sides. The sum of all the interior angles of a nonagon is equal to 1260 degrees.

The below-attached figure shows the shape of a nonagon that has 9 sides.

Angle for regular nonagon[tex]=\frac{360^{\circ}-40^{\circ}}{9}[/tex]

[tex]\therefore[/tex]Area of [tex]\bigtriangleup[/tex] OAB[tex]=\frac{1}{2}\times14\times14\times sin40[/tex]

                          [tex]=62.99 \ in^{2}[/tex]

Since there are 9 such triangles in a nonagon.

Total area[tex]=9\times62.99 \ in^{2}[/tex]

                [tex]=567 \ in^{2}[/tex]

Below-attached is the diagram of [tex]\bigtriangleup[/tex] OAB.

Learn more about the topic of Nonagon: https://brainly.com/question/6644400

${teks-lihat-gambar} Omm2
${teks-lihat-gambar} Omm2

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