1. **Problem statement:** A rectangle is divided into four smaller rectangles. Three of them have areas 6 cm², 18 cm², and 36 cm². We need to find the area of the shaded rectangle. 2. **Understanding the problem:** Let the rectangle be divided into two rows and two columns, forming four smaller rectangles. Suppose the widths of the two columns are $x$ and $y$, and the heights of the two rows are $a$ and $b$. 3. **Assign areas:** The four rectangles have areas: - Top-left: $x \times a = 6$ - Top-right: $y \times a = 18$ - Bottom-left: $x \times b = 36$ - Bottom-right (shaded): $y \times b = ?$ 4. **Find $x$ and $y$ in terms of $a$:** From the top row: $$x = \frac{6}{a}, \quad y = \frac{18}{a}$$ 5. **Find $b$ using bottom-left area:** $$x \times b = 36 \implies b = \frac{36}{x} = \frac{36}{6/a} = \frac{36a}{6} = 6a$$ 6. **Calculate shaded area:** $$y \times b = \frac{18}{a} \times 6a = 18 \times 6 = 108$$ 7. **Check for consistency:** The shaded area is $108$ cm², which is not among the options. This suggests the assumption that the rectangle is divided into two rows and two columns is incorrect. 8. **Alternative approach:** The problem states the rectangle is divided into four smaller rectangles with areas 6, 18, 36, and the shaded one unknown. The figure likely divides the rectangle into two rows and two columns, but the arrangement of known areas is different. 9. **Let the widths be $x$ and $y$, heights be $a$ and $b$. Suppose the areas are arranged as: - Top-left: 6 - Top-right: 18 - Bottom-left: shaded area $S$ - Bottom-right: 36 10. **From top row:** $$x \times a = 6, \quad y \times a = 18 \implies y = 3x$$ 11. **From bottom row:** $$x \times b = S, \quad y \times b = 36$$ 12. **Express $b$ from bottom-right:** $$b = \frac{36}{y} = \frac{36}{3x} = \frac{12}{x}$$ 13. **Calculate $S$:** $$S = x \times b = x \times \frac{12}{x} = 12$$ 14. **Answer:** The shaded rectangle area is $12$ cm². **Final answer:** (C) 12 cm²