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?
To find the surface area of the room that needs to be painted, we need to calculate the surface area of each wall (including the walls, floor, and ceiling) separately and then add them all up.
1. Floor and Ceiling:
Since the room is rectangular, the floor and ceiling have the same dimensions as the room itself. Therefore, the surface area of the floor and ceiling is:
Surface area of floor = Length x Width = 20 ft x 15 ft = 300 sq. ft
Surface area of ceiling = Length x Width = 20 ft x 15 ft = 300 sq. ft
Total surface area of floor and ceiling = 300 sq. ft + 300 sq. ft = 600 sq. ft
2. Walls:
There are 4 walls in Monica's room (front wall, back wall, left wall, and right wall). Two of these walls have the dimensions of 20 ft x 9 ft (front and back walls), and the other two have the dimensions of 15 ft x 9 ft (left and right walls). Therefore, the surface area of each wall is:
Front and back walls = 2 x (Length x Height) = 2 x (20 ft x 9 ft) = 360 sq. ft
Left and right walls = 2 x (Width x Height) = 2 x (15 ft x 9 ft) = 270 sq. ft
Total surface area of walls = 360 sq. ft + 270 sq. ft = 630 sq. ft
Adding the surface area of the floor and ceiling to the surface area of the walls:
Total surface area = 600 sq. ft + 630 sq. ft = 1230 sq. ft
Therefore, the total surface area of Monica's room that needs to be painted, including the floor and ceiling, is 1230 square feet.