To find the surface area of Monica's room that is going to be painted, we need to calculate the area of the walls, the ceiling, and the floor.
1. Calculate the area of the ceiling: The ceiling is a rectangle with dimensions equal to the length and width of the room.
- Area of the ceiling = length × width
- Area of the ceiling = 20 ft × 15 ft = 300 ft²
2. Calculate the area of the floor: The floor also has the same dimensions as the ceiling.
- Area of the floor = length × width
- Area of the floor = 20 ft × 15 ft = 300 ft²
3. Calculate the area of the walls: There are four walls in the room, and we can divide them into two sets of opposite walls:
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Two walls with dimensions of length and height:
- Area of one wall = length × height = 20 ft × 9 ft = 180 ft²
- Area of two walls = 2 × 180 ft² = 360 ft²
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Two walls with dimensions of width and height:
- Area of one wall = width × height = 15 ft × 9 ft = 135 ft²
- Area of two walls = 2 × 135 ft² = 270 ft²
Now, add the areas of the walls together:
- Total area of walls = 360 ft² + 270 ft² = 630 ft²
4. Add the areas of the ceiling, floor, and walls:
- Total surface area = area of ceiling + area of floor + total area of walls
- Total surface area = 300 ft² + 300 ft² + 630 ft² = 1230 ft²
The total surface area of the room that will be painted (including the floor and ceiling) is:
\[ \text{Surface area} = 1230 \text{ square feet} \]