To find the surface area of Monica's room that will be painted, we need to calculate the areas of the four walls, the floor, and the ceiling.
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Calculate the area of the four walls:
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The room has two pairs of walls. The area of each pair can be calculated as follows:
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Area of the two longer walls (length): \[ \text{Area} = 2 \times (\text{length} \times \text{height}) = 2 \times (20 , \text{ft} \times 9 , \text{ft}) = 2 \times 180 , \text{ft}^2 = 360 , \text{ft}^2 \]
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Area of the two shorter walls (width): \[ \text{Area} = 2 \times (\text{width} \times \text{height}) = 2 \times (15 , \text{ft} \times 9 , \text{ft}) = 2 \times 135 , \text{ft}^2 = 270 , \text{ft}^2 \]
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Total area of the walls: \[ \text{Total wall area} = 360 , \text{ft}^2 + 270 , \text{ft}^2 = 630 , \text{ft}^2 \]
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Calculate the area of the floor: \[ \text{Floor area} = \text{length} \times \text{width} = 20 , \text{ft} \times 15 , \text{ft} = 300 , \text{ft}^2 \]
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Calculate the area of the ceiling: \[ \text{Ceiling area} = \text{length} \times \text{width} = 20 , \text{ft} \times 15 , \text{ft} = 300 , \text{ft}^2 \]
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Total surface area to be painted: \[ \text{Total surface area} = \text{Total wall area} + \text{Floor area} + \text{Ceiling area} \] \[ \text{Total surface area} = 630 , \text{ft}^2 + 300 , \text{ft}^2 + 300 , \text{ft}^2 = 1230 , \text{ft}^2 \]
Therefore, the surface area of the room that Monica is going to paint is 1230 square feet.