Subjects geometry

Rectangle Frame 09D577

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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**.