Subjects geometry

Paint Quarts B0673A

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1. **State the problem:** We need to find how many quarts of paint are required to paint the ramp with two coats, excluding the bottom. 2. **Identify the surface area to be painted:** The ramp is a prism-like shape with given edges: slanted edge 15.2 ft, bottom-left edge 19.5 ft, bottom center edge 14 ft, and right vertical edge 6 ft. 3. **Calculate the surface area of the ramp excluding the bottom:** - The ramp has 3 visible faces: the slanted rectangular face, the vertical rectangular face, and the rectangular base (excluding the bottom). 4. **Calculate each face area:** - Slanted face area = length × height = 15.2 ft × 6 ft = $$15.2 \times 6 = 91.2$$ sq ft - Vertical face area = width × height = 14 ft × 6 ft = $$14 \times 6 = 84$$ sq ft - Bottom face area (top rectangle) = length × width = 15.2 ft × 14 ft = $$15.2 \times 14 = 212.8$$ sq ft 5. **Total surface area to paint (excluding bottom):** $$91.2 + 84 + 212.8 = 388$$ sq ft 6. **Since two coats are needed, multiply total area by 2:** $$388 \times 2 = 776$$ sq ft 7. **Calculate the number of quarts needed:** - One quart covers 80 sq ft. - Number of quarts = $$\frac{776}{80} = 9.7$$ 8. **Since you cannot buy a fraction of a quart, round up:** - Quarts to buy = 10 **Final answer:** You should buy 10 quarts of paint.
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