For Monica’s 14th birthday, she wants to make over her bedroom. The first phase in the bedroom makeover is painting her room. If Monica’s room is 20 ft. long, 15 ft. wide, and 9 ft. high, find the surface area of the room that you are going to paint, including the floor and ceiling(1 point) surface area= square feet

1 answer

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.

  1. Calculate the area of the four walls:

    • The room has two pairs of walls. The area of each pair can be calculated as follows:

      • Area of the two longer walls (length): \[ \text{Area} = 2 \times (\text{length} \times \text{height}) = 2 \times (20 , \text{ft} \times 9 , \text{ft}) = 2 \times 180 , \text{ft}^2 = 360 , \text{ft}^2 \]

      • Area of the two shorter walls (width): \[ \text{Area} = 2 \times (\text{width} \times \text{height}) = 2 \times (15 , \text{ft} \times 9 , \text{ft}) = 2 \times 135 , \text{ft}^2 = 270 , \text{ft}^2 \]

    • Total area of the walls: \[ \text{Total wall area} = 360 , \text{ft}^2 + 270 , \text{ft}^2 = 630 , \text{ft}^2 \]

  2. Calculate the area of the floor: \[ \text{Floor area} = \text{length} \times \text{width} = 20 , \text{ft} \times 15 , \text{ft} = 300 , \text{ft}^2 \]

  3. Calculate the area of the ceiling: \[ \text{Ceiling area} = \text{length} \times \text{width} = 20 , \text{ft} \times 15 , \text{ft} = 300 , \text{ft}^2 \]

  4. 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.