Question 12
There are four rectangular pieces with dimensions of $1\ \mathrm{cm}\times2\ \mathrm{cm}$ , $3\ \mathrm{cm}\times4\ \mathrm{cm}$ , $5\ \mathrm{cm}\times6\ \mathrm{cm}$ and $7\ \mathrm{cm}\times8\ \mathrm{cm}$ respectively. They are to be placed on a larger rectangular graphing paper without overlapping. The sides of each piece should be parallel to the edges of the graph paper and that one vertex from each of the four pieces should coincide at a point (that is, this point is also the vertex of four rectangles). What is the smallest possible area, in cm² , of the graphing paper?