A decoupage problem consists of cutting up one figure in order to reassemble its pieces in the shape of another figure. A closely related problem is one of assembling, starting with several figures of identical shape and then cutting them into pieces as economically as possible in order to reconstruct a similar figure of greater size.
Can you cut these three little octagons into a total of ten pieces and then reconstruct a single octagon with three times the area?
The dimensions of the little octagons must be multiplied by in order to obtain the big octagon with three times the surface. It is therefore necessary to produce the hypotenuse of a right triangle with sides and . The rest is inspired trial and error. (See Greg Frederickson, “More Geometric Dissections,” Journal of Recreational Mathematics [Summer 1974].)