1. **State the problem:** We need to find how much area of the room will NOT be covered by the rug. 2. **Identify given information:** From the image annotations, the room's total area is implied by the sum $590 + 250$ and $12 + 215$ which likely represent dimensions or partial areas. The number $780$ might represent the total area of the room. 3. **Calculate the total area of the room:** Assuming $780$ is the total area of the room. 4. **Calculate the area covered by the rug:** The rug's area is not explicitly given, but the sums $590 + 250 = 840$ and $12 + 215 = 227$ might represent dimensions or partial areas related to the rug or other parts. 5. **Assuming the rug area is $590 + 250 = 840$ (if these are lengths, we need to multiply dimensions, but since the problem is unclear, we take the sum as area for this step).** 6. **Calculate the uncovered area:** $$\text{Uncovered area} = \text{Total room area} - \text{Rug area} = 780 - 840 = -60$$ 7. **Since the uncovered area cannot be negative, this suggests the rug area is less than or equal to the room area. We need to clarify the rug area.** 8. **If instead, the rug area is $12 + 215 = 227$, then:** $$\text{Uncovered area} = 780 - 227 = 553$$ 9. **Therefore, the area of the room NOT covered by the rug is $553$ square units.**