To calculate the area to be painted and the cost, we will follow these steps:
- Calculate the total surface area of the walls in the school hall.
- Calculate the area of the windows.
- Calculate the area of the doors.
- Subtract the area of the windows and doors from the total wall area to find the area that needs to be painted.
- Calculate the cost of painting the walls based on the area to be painted.
Step 1: Total Surface Area of the Walls
The school hall has four walls. We calculate the area of each pair of opposite walls:
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Two walls that are 16.4 m long and 4 m high: \[ \text{Area} = 2 \times (16.4, \text{m} \times 4, \text{m}) = 2 \times 65.6, \text{m}^2 = 131.2, \text{m}^2 \]
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Two walls that are 8 m wide and 4 m high: \[ \text{Area} = 2 \times (8, \text{m} \times 4, \text{m}) = 2 \times 32, \text{m}^2 = 64, \text{m}^2 \]
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Total area of the walls: \[ \text{Total wall area} = 131.2, \text{m}^2 + 64, \text{m}^2 = 195.2, \text{m}^2 \]
Step 2: Area of the Windows
Each window measures 1.25 m by 1.8 m, and there are 4 windows: \[ \text{Area of one window} = 1.25, \text{m} \times 1.8, \text{m} = 2.25, \text{m}^2 \] \[ \text{Total area of windows} = 4 \times 2.25, \text{m}^2 = 9, \text{m}^2 \]
Step 3: Area of the Doors
Each door measures 2.5 m by 1 m, and there are 2 doors: \[ \text{Area of one door} = 2.5, \text{m} \times 1, \text{m} = 2.5, \text{m}^2 \] \[ \text{Total area of doors} = 2 \times 2.5, \text{m}^2 = 5, \text{m}^2 \]
Step 4: Calculate the Area to be Painted
To find the area that needs to be painted, we subtract the areas of the windows and doors from the total wall area: \[ \text{Area to be painted} = \text{Total wall area} - (\text{Total area of windows} + \text{Total area of doors}) \] \[ \text{Area to be painted} = 195.2, \text{m}^2 - (9, \text{m}^2 + 5, \text{m}^2) = 195.2, \text{m}^2 - 14, \text{m}^2 = 181.2, \text{m}^2 \]
Step 5: Calculate the Cost of Painting
If the cost of painting per square meter is 120 shillings, then: \[ \text{Cost} = \text{Area to be painted} \times \text{Cost per square meter} \] \[ \text{Cost} = 181.2, \text{m}^2 \times 120, \text{shillings/m}^2 = 21744, \text{shillings} \]
Final Results
- Area of the windows: 9 m²
- Cost to paint the walls: 21,744 shillings