Long Descriptions for Chapter Nine

Figure 9.1: Border Problem

Six rectangles include two squares each. Squares include borders comprising various shadings. Rectangle one includes two squares shaded to indicate 10 + 10 + 8 + 8 and n + (n – 2) + n + n (n – 2). Rectangle two includes two squares shaded 10 + 9 + 9 + 8 and n + 2(n – 1) + (n – 2). Rectangle three includes two squares shaded 4 × 8 + 4 and 4(n – 2) + 4. Rectangle five includes two squares shaded 9 + 9 + 9 + 9 = 9 × 4 and (n – 1) × 4. Rectangle five includes two squares shaded 4 × 10 – 4 and 4n – 4. Rectangle six includes two squares shaded (10 × 10) – (8 × 8) and n squared – (n – 2) squared.