Subjects geometry

Rectangle Frame D767D5

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1. **Problem Statement:** Find the area of the shaded region which is the inner rectangle framed by a 2-unit wide frame inside an outer rectangle of width 12 units and height 8 units. 2. **Understanding the problem:** The outer rectangle has dimensions width = 12 and height = 8. The frame around the inner rectangle is 2 units wide on all sides. 3. **Formula for area of a rectangle:** $$\text{Area} = \text{width} \times \text{height}$$ 4. **Calculate dimensions of the inner rectangle:** Since the frame is 2 units wide on each side, the inner rectangle's width is: $$12 - 2 - 2 = 12 - 4 = 8$$ Similarly, the inner rectangle's height is: $$8 - 2 - 2 = 8 - 4 = 4$$ 5. **Calculate the area of the inner rectangle (shaded region):** $$\text{Area}_{\text{shaded}} = 8 \times 4 = 32$$ 6. **Final answer:** The area of the shaded region is $32$ square units.