Problem $1$

A regular polygon is a polygon that is direct equiangular $($all angles are equal in measure$)$ and equilateral $($all sides have the same length$).$ The vertices of a regular polygon fall on a circle of radius $r$ at equal angular separation. For example, a $3-$sided polygon is an equilateral triangle, which can be constructed by connecting lines between vertices located along a circle at $0,120,$ and $240$ degrees.

Write a program that:

Asks the user for a number between $3$ and $13.$ This will represent the number of sides in a regular polygon.

Asks the user for three numbers between $0$ and $1.$ These will represent an RGB triplet vector identifying a color to be used in constructing a regular polygon.

Define the vertex points for the polygon. The distance of each vertex from the origin will be $10,$ and there will always be a vertex on the $+y-$axis.

Construct an RGB triplet vector representing a color using the three numbers entered by the user.

Use the fill$()$ function to plot the polygon in a figure with the user$-$selected color. The polygon border should be black with a linewidth of $2.$

Do not display the figure axes, but do display a pithy title for the figure different from the example shown below. Ensure that your figure has an aspect ratio of $1$:$1.$

Using the num$2$str$()$ function, create a character string that says $"$A x sided polygon" where $x$ is replaced by the number of sides selected by the user. Use MATLAB's help function to determine the syntax for the num$2$str$()$ function. Then print this text such that it is vertically located at $y=0$ and is approximately centered horizontally.