the procedure to follow consists in reducing the given polygon to another equivalent, with one side less. This will be done as many times as necessary, until there is a triangle.
First, join the vertices, A and E.
Second, make a parallel to this previous union, by the common vertex, F.
And third, to extend the side, AB, until cutting to the parallel of the vertex F, in the new vertex A.
The same procedure is followed to eliminate the vertices C, and D.
we obtain a triangle equivalent to the given polygon.
TRIANGLE EQUIVALENT TO A HEXAGON.
WE APPLY THE SAME METHOD.
DRAWING OF A SQUARE EQUIVALENT TO A REGULAR PENTAGON
We must transform the pentagon into an equivalent triangle.
First, join the vertices, 1 with 4.
Second, make a parallel to this previous union, by the common vertex, 5.
The same procedure is followed with vertices 1, 3 and 2.
And third, to extend the horizontal side of the pentagon, until cutting to the parallels in the new vertices M and A.
In this way, we draw a triangle equivalent to the given polygon.
We find half the height of this triangle.
We add to its base this half of the height.
We locate the midpoint of the sum of these segments.
With center at this midpoint, a semicircle is drawn.
We raise a perpendicular from A, which will cut to the semicircle at point B, giving us the side of the square we are looking for, A B.