To calculate the surface area of Monica's room that includes the walls, floor, and ceiling, you can use the following steps:
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Calculate the area of the four walls:
- The two longer walls (length x height): \[ 2 \times (20 , \text{ft} \times 9 , \text{ft}) = 2 \times 180 , \text{ft}^2 = 360 , \text{ft}^2 \]
- The two shorter walls (width x height): \[ 2 \times (15 , \text{ft} \times 9 , \text{ft}) = 2 \times 135 , \text{ft}^2 = 270 , \text{ft}^2 \]
- 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:
- The ceiling area is the same as the floor area: \[ \text{Ceiling area} = 300 , \text{ft}^2 \]
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Calculate the total surface area to be painted: \[ \text{Total surface area} = \text{Total wall area} + \text{Floor area} + \text{Ceiling area} \] \[ = 630 , \text{ft}^2 + 300 , \text{ft}^2 + 300 , \text{ft}^2 = 1230 , \text{ft}^2 \]
Therefore, the total surface area of the room that you are going to paint is 1230 square feet.