Question 71
A convex polygon is called elegant if it can be decomposed into equilateral triangles, squares, or both, all with the same side length. Below are examples, with a decomposition and the number of sides shown for each.
4 sides
5 sides
6 sides
7 sides
a) Draw an elegant polygon with 8 sides, indicating a decomposition.
b) What are the possible measures of interior angles of an elegant polygon?
c) Show that an elegant polygon cannot have more than 12 sides.
d) Draw an elegant polygon with 12 sides, indicating a decomposition.
4 sides
5 sides
6 sides
7 sides
a) Draw an elegant polygon with 8 sides, indicating a decomposition.
b) What are the possible measures of interior angles of an elegant polygon?
c) Show that an elegant polygon cannot have more than 12 sides.
d) Draw an elegant polygon with 12 sides, indicating a decomposition.