The area of a regular nonagon is \(567 \ in^{2}\).
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\(=\frac{360^{\circ}-40^{\circ}}{9}\)
\(\therefore\)Area of \(\bigtriangleup\) OAB\(=\frac{1}{2}\times14\times14\times sin40\)
\(=62.99 \ in^{2}\)
Since there are 9 such triangles in a nonagon.
Total area\(=9\times62.99 \ in^{2}\)
\(=567 \ in^{2}\)
Below-attached is the diagram of \(\bigtriangleup\) OAB.
Learn more about the topic of Nonagon: https://brainly.com/question/6644400
