Given a sufficiently large supply of equilateral triangles and squares, all with the same side length. From these building blocks, convex* polygons can be formed by placing them seamlessly and without overlap in the plane. (The figure shows three possibilities for a hexagon.)
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a) What is the maximum possible number of side edges for a convex polygon formed in this way? (The answer must be justified.)
b) Provide examples for all possible numbers of side edges .
*) A figure is called convex if for any two of its points, all points on the connecting line segment also belong to the figure.
Solution
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