D6. Rectangle Pinwheel

Contributed by Arsalan Wares, Valdosta State University

Figure 2: A pinwheel made of 16 rectangles.

The outermost polygon shown in figure 2 as the region shaded in pink consists of 16 congruent rectangles placed so that their edges align (and vertices of four of the rectangles coincide at the center of the polygon). We call this polygon a 28-gon because it has 28 edges: the line segments that make up its boundary. The perimeter of each rectangle is 26 cm and the perimeter of the 28-gon is 136 cm. What is the area of the 28-gon?

This problem originally appeared in the Prisoner’s Dilemma in the 2022 Summer issue of the PMP Newsletter. Solutions will be accepted through 2022 Sep 1.