1. **State the problem:** We need to find the area of a stained glass window shaped like a rectangle with a quarter circle cut out from the top right corner, and a square inside that quarter circle. 2. **Identify the shapes and dimensions:** - Rectangle: width = 16 in, height = 10 in - Quarter circle radius = 4 in - Square side length = 4 in (inside the quarter circle) 3. **Calculate the area of the rectangle:** $$\text{Area}_{rectangle} = \text{width} \times \text{height} = 16 \times 10 = 160$$ 4. **Calculate the area of the quarter circle:** The area of a full circle is $$\pi r^2$$, so the quarter circle area is $$\frac{1}{4} \pi r^2$$. $$\text{Area}_{quarter circle} = \frac{1}{4} \times 3.14 \times 4^2 = \frac{1}{4} \times 3.14 \times 16 = 12.56$$ 5. **Calculate the area of the square inside the quarter circle:** $$\text{Area}_{square} = 4 \times 4 = 16$$ 6. **Find the area of the window:** The quarter circle area is removed from the rectangle, but the square inside the quarter circle is part of the window, so we add it back. $$\text{Area}_{window} = \text{Area}_{rectangle} - \text{Area}_{quarter circle} + \text{Area}_{square}$$ $$= 160 - 12.56 + 16 = 163.44$$ 7. **Round to the nearest tenth:** $$163.44 \approx 163.4$$ **Final answer:** The area of the window is **163.4 in.^2**.