Subjects geometry

Window Area C6Ad53

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1. **State the problem:** We have a large stained glass window and a smaller scale drawing of it. The actual window has an area of 680 m². We need to find the area of the scale drawing in m², rounded to 3 decimal places. 2. **Identify the scale factor:** The actual window height is 28 m, and the drawing height is 70 cm = 0.7 m. 3. **Calculate the linear scale factor:** $$\text{scale factor} = \frac{\text{drawing height}}{\text{actual height}} = \frac{0.7}{28} = 0.025$$ 4. **Use the area scale factor:** Areas scale by the square of the linear scale factor. $$\text{area scale factor} = (0.025)^2 = 0.000625$$ 5. **Calculate the drawing area:** $$\text{drawing area} = \text{actual area} \times \text{area scale factor} = 680 \times 0.000625 = 0.425$$ 6. **Round the answer:** $$0.425 \text{ m}^2$$ **Final answer:** The area of the drawing is **0.425 m²** to 3 decimal places.
Actual window 28 mDrawing 70 cm