How to divide a regular pentagon into 3 equal parts?

Question

Geometry

With a mathematical solution (with all the evidence) and a drawing, of course.

Answer 1

Take the center of the inscribed (and circumscribed) circle. Divide each side into 3 equal parts. Draw lines from the center to all 5 vertices and 10 points on the sides. You will get 15 triangles, with the same outer sides (1/3 of the side of the pentagon). All these triangles also have the same heights (the radius of the inscribed circle). Therefore, they are all the same area. Now break them into 3 groups of 5 consecutive triangles - here are your 3 pieces of the pentagon, equal in area.
This works not only for regular pentagons - it is enough to be able to fit a circle into a polygon. Then draw segments from the center of the inscribed circle to the border so that the lengths of the perimeters of the resulting parts are the same. The areas will be equal to the lengths of the perimeter * the radius of the circle in half.