Question:

<p><strong>Step 1:</strong> Use the formula for rectangles in an n × p rectangle (n < p):</p><p>Number of rectangles = $$\frac{np(n+1)(p+1)}{4}$$</p><p><strong>Step 2:</strong> Here n = 6 and p = 9, so:</p><p>Number of rectangles = $$\frac{6 \cdot 9 \cdot (6+1) \cdot (9+1)}{4} = \frac{6 \cdot 9 \cdot 7 \cdot 10}{4} = 945$$</p><p><strong>Step 3:</strong> Find number of squares using:</p><p>$$\sum_{r=1}^{6} (7-r)(10-r) = \sum_{r=1}^{6} (70 - 17r + r^2) = 154$$</p><p><strong>Step 4:</strong> Number of rectangles excluding squares = 945 - 154 = 791</p>