To find the surface area of Monica's room that needs to be painted, we need to calculate the surface area of the walls, ceiling, and floor.
Step 1: Calculate the area of the floor and ceiling.
The floor and ceiling are both rectangles with the same dimensions.
- Length = 20 ft
- Width = 15 ft
Area of the floor (or ceiling) = Length × Width = 20 ft × 15 ft = 300 sq ft
Since there are both a floor and a ceiling:
Combined area of the floor and ceiling = 2 × Area of one = 2 × 300 sq ft = 600 sq ft
Step 2: Calculate the area of the four walls.
- Two walls will have dimensions of 20 ft (length) × 9 ft (height)
- The other two walls will have dimensions of 15 ft (width) × 9 ft (height)
Area of the two length walls: \[ 2 \times (20 ft \times 9 ft) = 2 \times 180 sq ft = 360 sq ft \]
Area of the two width walls: \[ 2 \times (15 ft \times 9 ft) = 2 \times 135 sq ft = 270 sq ft \]
Total area of the walls: \[ 360 sq ft + 270 sq ft = 630 sq ft \]
Step 3: Calculate the total surface area to be painted.
Total surface area = Area of the floor and ceiling + Total area of the walls \[ 600 sq ft + 630 sq ft = 1230 sq ft \]
So, the total surface area that will be painted is: \[ \text{Surface area} = 1230 \text{ square feet} \]