1. **State the problem:**
We have two rectangles, one inside the other. The outer rectangle has dimensions 12 units by 9 units.
The inner rectangle is framed inside the outer one with a frame thickness of 1 unit all around.
We need to find the area of the shaded region, which is the area of the outer rectangle minus the area of the inner rectangle.
2. **Formula and explanation:**
The area of a rectangle is given by the formula:
$$\text{Area} = \text{width} \times \text{height}$$
Since the frame is 1 unit thick on all sides, the inner rectangle's width and height are each reduced by 2 units (1 unit on each side).
3. **Calculate the dimensions of the inner rectangle:**
$$\text{Inner width} = 12 - 2 = 10$$
$$\text{Inner height} = 9 - 2 = 7$$
4. **Calculate the areas:**
Outer rectangle area:
$$12 \times 9 = 108$$
Inner rectangle area:
$$10 \times 7 = 70$$
5. **Calculate the shaded area:**
$$\text{Shaded area} = 108 - 70 = 38$$
**Final answer:**
The area of the shaded region is **38 square units**.
Rectangle Frame 09D577
Step-by-step solutions with LaTeX - clean, fast, and student-friendly.