1. **State the problem:** We need to find the area of a composite figure made by joining two rectangles. 2. **Identify the rectangles and their dimensions:** - Bottom rectangle: width = 75 in, height = 15 in - Top smaller rectangle (centered): width = 25 in, height = 10 in - Two side rectangles (attached to bottom rectangle on either side of the top rectangle): each width = 25 in, height = 15 in 3. **Formula for area of a rectangle:** $$\text{Area} = \text{width} \times \text{height}$$ 4. **Calculate the area of each rectangle:** - Bottom rectangle area: $$75 \times 15 = 1125$$ - Top smaller rectangle area: $$25 \times 10 = 250$$ - Each side rectangle area: $$25 \times 15 = 375$$ 5. **Calculate total area:** The figure is composed of the bottom rectangle plus the top smaller rectangle plus the two side rectangles. $$\text{Total area} = 1125 + 250 + 2 \times 375$$ 6. **Simplify:** $$2 \times 375 = 750$$ $$\text{Total area} = 1125 + 250 + 750 = 2125$$ **Final answer:** $$\boxed{2125}$$ square inches