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 feet long 15 feet wide and 9 feet high find the surface area of the room that you are going to paint include the floor and the ceiling.
2(20+15)*9 + 2*20*15 = 1230
not counting the doors or windows
To find the surface area of the room that needs to be painted, we need to calculate the area of each wall, the floor, and the ceiling separately, and then sum them up.
1. Start with the floor:
The surface area of the floor is simply the length multiplied by the width:
Floor Area = Length × Width
Given that Monica's room is 20 feet long and 15 feet wide:
Floor Area = 20 ft × 15 ft
2. Next, calculate the area of each wall:
You need to find the area of each of the four walls in the room. To do this, you'll multiply the height of the room by the total length of each wall.
Wall 1: Length × Height
Wall 2: Length × Height
Wall 3: Width × Height
Wall 4: Width × Height
For Wall 1 and Wall 2, we use the length of the room (20 feet) and the height (9 feet):
Wall 1 and Wall 2 Area = 20 ft × 9 ft
For Wall 3 and Wall 4, we use the width of the room (15 feet) and the height (9 feet):
Wall 3 and Wall 4 Area = 15 ft × 9 ft
3. Finally, calculate the ceiling area:
The ceiling area is equal to the length multiplied by the width:
Ceiling Area = Length × Width
Given that Monica's room is 20 feet long and 15 feet wide:
Ceiling Area = 20 ft × 15 ft
To get the total surface area, sum up the measurements of the floor, ceiling, and all four walls:
Total Surface Area = Floor Area + (2 × Wall 1 and Wall 2 Area) + (2 × Wall 3 and Wall 4 Area) + Ceiling Area
Once you have the values for each area, substitute them in the equation and compute the result.
To find the surface area of the room that needs to be painted, we need to calculate the area of all the walls, the floor, and the ceiling.
1. Start by calculating the area of the floor:
The floor area can be found by multiplying the length and width of the room.
Floor area = Length × Width
Given: Length = 20 feet, Width = 15 feet
Floor area = 20 ft × 15 ft = 300 square feet
2. Next, calculate the area of the ceiling:
The ceiling area is also found by multiplying the length and width of the room.
Ceiling area = Length × Width
Given: Length = 20 feet, Width = 15 feet
Ceiling area = 20 ft × 15 ft = 300 square feet
3. Now, calculate the total area of the four walls:
The total area of all four walls can be calculated by adding the areas of each wall.
a. The area of the front and back walls:
To find the area of each wall, multiply the width of the room by the height.
Front/Back wall area = Width × Height
Given: Width = 15 feet, Height = 9 feet
Front/Back wall area = 15 ft × 9 ft = 135 square feet
b. The area of the two side walls:
To find the area of each side wall, multiply the length of the room by the height.
Side wall area = Length × Height
Given: Length = 20 feet, Height = 9 feet
Side wall area = 20 ft × 9 ft = 180 square feet
Total area of the four walls = 2 × (Front/Back wall area) + 2 × (Side wall area)
= 2 × 135 sq ft + 2 × 180 sq ft
= 270 sq ft + 360 sq ft
= 630 square feet
4. Finally, calculate the total surface area to be painted:
Adding up the floor area, ceiling area, and wall area will give the total surface area to be painted.
Total surface area = Floor area + Ceiling area + Total area of the walls
= 300 sq ft + 300 sq ft + 630 sq ft
= 1230 square feet
Therefore, the surface area of Monica's room that needs to be painted, including the floor and ceiling, is 1230 square feet.