Answer :
To determine the total surface area to be painted in the classroom, we need to calculate the area of the walls and the ceiling, and then subtract the areas of the door and the windows, as these will not be painted.
Step 1: Calculate the Area of the Walls
The classroom is a rectangular prism with dimensions 6m by 6m by 3m. To find the total area of the four walls, calculate both pairs of opposite walls and add them together.
Front and Back Walls: Each wall has dimensions 6m (width) by 3m (height). Therefore, the area for one wall is:
[tex]\text{Area of one wall} = 6 \times 3 = 18 \text{ m}^2[/tex]
Since there are two such walls:
[tex]\text{Total area of front and back walls} = 2 \times 18 = 36 \text{ m}^2[/tex]
Side Walls: Each side wall has dimensions 6m (length) by 3m (height). The area for one side wall is:
[tex]\text{Area of one side wall} = 6 \times 3 = 18 \text{ m}^2[/tex]
Similarly, for two walls:
[tex]\text{Total area of side walls} = 2 \times 18 = 36 \text{ m}^2[/tex]
Total Wall Area:
[tex]\text{Total wall area} = 36 + 36 = 72 \text{ m}^2[/tex]
Step 2: Calculate the Area of the Ceiling
The ceiling is a flat surface with dimensions 6m by 6m.
Ceiling Area:
[tex]\text{Ceiling area} = 6 \times 6 = 36 \text{ m}^2[/tex]
Step 3: Calculate Total Area to be Painted
Add the wall area and the ceiling area:
Total Surface Area (before subtracting openings):
[tex]\text{Total surface area} = 72 + 36 = 108 \text{ m}^2[/tex]
Step 4: Subtract the Areas of the Door and Windows
Door Area:
[tex]\text{Door area} = 0.9 \times 2 = 1.8 \text{ m}^2[/tex]
Windows Area: Each window measures 1.5m by 1.2m, and there are four windows. Therefore:
[tex]\text{Area of one window} = 1.5 \times 1.2 = 1.8 \text{ m}^2[/tex]
[tex]\text{Total windows area} = 4 \times 1.8 = 7.2 \text{ m}^2[/tex]
Total Area to Subtract:
[tex]\text{Total area of door and windows} = 1.8 + 7.2 = 9 \text{ m}^2[/tex]
Final Step: Calculate the Total Surface Area to be Painted
Subtract the area of the door and windows from the total surface area:
Total Surface Area to be Painted:
[tex]\text{Surface area to be painted} = 108 - 9 = 99 \text{ m}^2[/tex]
Therefore, the total surface area to be painted is 99 square meters.
