1. **Problem statement:** The areas of a circle and a rectangle are equal, and the area of the shaded region (the overlapping part) is 10 cm². We need to find the area of the rectangle. 2. **Understanding the problem:** Let the area of the circle be $A_c$ and the area of the rectangle be $A_r$. Given that $A_c = A_r$ and the shaded region area is 10 cm². 3. **Key formula:** Since the shaded region is the overlap of the circle and rectangle, and the areas are equal, the total area of the rectangle is the sum of the shaded region and the non-overlapping part. 4. **Given options:** a) 40 cm², b) 30 cm², c) 60 cm², d) 75 cm². 5. **Reasoning:** The shaded region is part of both shapes, so the rectangle's area must be larger than the shaded region. Since the circle and rectangle have equal areas, and the shaded region is 10 cm², the rectangle's area must be equal to the circle's area. 6. **Conclusion:** The rectangle's area equals the circle's area, and the shaded region is 10 cm². The only option that fits the problem context (area larger than shaded region and equal to circle) is 30 cm². **Final answer:** 30 cm²