https://file.aiquickdraw.com/mathbot/file/17289289863981fq6yyd7.jpg

To solve this problem, we need to determine the area of the shaded region between the two rectangles. Here's the step-by-step process:

1. **Dimensions of the Inner Rectangle:**
   - Length: 12 units
   - Width: 9 units

2. **Dimensions of the Outer Rectangle:**
   - Since the frame is 1 unit wide, we add 1 unit to each side of the inner rectangle to get the outer rectangle's dimensions.
   - Length: \( 12 + 2 \times 1 = 12 + 2 = 14 \) units
   - Width: \( 9 + 2 \times 1 = 9 + 2 = 11 \) units

3. **Area Calculations:**
   - Area of the Inner Rectangle: \( 12 \times 9 = 108 \) square units
   - Area of the Outer Rectangle: \( 14 \times 11 = 154 \) square units

4. **Shaded Area Calculation:**
   - Shaded Area = Area of the Outer Rectangle - Area of the Inner Rectangle
   - \( 154 - 108 = 46 \) square units

Thus, the area of the shaded region is \( 46 \) square units.

Do you want more details or have any questions? Here are some related questions you might find useful:

1. How would the area of the shaded region change if the frame width were 2 units instead of 1 unit?
2. What is the perimeter of the inner rectangle?
3. What is the perimeter of the outer rectangle?
4. How would you calculate the area of the shaded region if the inner rectangle were not centered within the outer rectangle?
5. Can you find a formula for the shaded area in terms of the inner rectangle's dimensions and the frame width?

**Tip:** Always double-check your dimensions and calculations to ensure accuracy when solving geometry problems.

One rectangle is 'framed' within another. Find the area of the shaded region if the 'frame' is 1 unit wide. The dimensions of the inner rectangle are 12 units by 9 units.

Learn how to calculate the area of the shaded region between two rectangles when one is framed inside the other with a frame width of 1 unit. This problem involves geometry and area calculation, suitable for students in Grades 6-8.

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