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)

Question

surface area=
square feet

Answer 1

To find the total surface area of Monica's room that will be painted, we will calculate the areas of the four walls, the ceiling, and the floor.

1. Walls:

   • There are two pairs of opposite walls.

   • The area of the two longer walls (20 ft. long and 9 ft. high): \( 2 \times (20 , \text{ft} \times 9 , \text{ft}) = 2 \times 180 , \text{sq ft} = 360 , \text{sq ft} \)

   • The area of the two shorter walls (15 ft. wide and 9 ft. high): \( 2 \times (15 , \text{ft} \times 9 , \text{ft}) = 2 \times 135 , \text{sq ft} = 270 , \text{sq ft} \)

   • Total wall area: \( 360 , \text{sq ft} + 270 , \text{sq ft} = 630 , \text{sq ft} \)

2. Ceiling:

   • The area of the ceiling (20 ft. long and 15 ft. wide): \( 20 , \text{ft} \times 15 , \text{ft} = 300 , \text{sq ft} \)

3. Floor:

   • The area of the floor (20 ft. long and 15 ft. wide): \( 20 , \text{ft} \times 15 , \text{ft} = 300 , \text{sq ft} \)

4. Total Surface Area:

   • Total area = Area of walls + Area of ceiling + Area of floor
   • Total area = \( 630 , \text{sq ft} + 300 , \text{sq ft} + 300 , \text{sq ft} \)
   • Total area = \( 630 , \text{sq ft} + 600 , \text{sq ft} = 1230 , \text{sq ft} \)

Therefore, the total surface area of the room that Monica is going to paint is 1230 square feet.