What is the number of rectangles in the following figure?

Step 1: Understand the figure

The figure is a large rectangle subdivided into smaller rectangles using horizontal and vertical lines.

We are to count all possible rectangles, including both individual blocks and combinations of adjacent blocks.

Step 2: Count individual rectangles

• Top row: 3 individual rectangles
• Right column: 2 individual rectangles
• Large central rectangle (bottom left): 1 individual rectangle

Total individual rectangles = 3 + 2 + 1 = 6

Step 3: Count composite rectangles (formed by combining blocks)

• Right vertical column (2 stacked rectangles) = 1 composite rectangle
• Top row: combining 2 top rectangles together = 1
• Entire top row (3 rectangles) = 1

Total composite rectangles = 1 + 1 + 1 = 3

Step 4: Add both

Total rectangles = 6 (individual) + 3 (composite) = 9 rectangles

Final Answer: 9 rectangles