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A school hall is equal to 16.4 m long 8 m wide and 4 m high the whole has four identical glass windows each measuring 1.25 m by 1.8 m and two doors each measuring 2.5 m by 1 m the inside walls were painted except the windows and the doors calculate the area of the worlds to be painted in square meters we how much will it cost to paint the walls if the cost of painting per meters Square is 120 shilling

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To determine the area of the walls that need to be painted, first, we need to calculate the total surface area of the walls in the school hall, subtract the areas of the windows and the doors from it.

Step 1: Calculate the total area of the walls

The hall is a rectangular prism, so the area of the walls can be calculated as follows:

  1. Calculate the perimeter of the hall:

    \[ \text{Perimeter} = 2 \times (\text{length} + \text{width}) = 2 \times (16.4 , \text{m} + 8 , \text{m}) = 2 \times 24.4 , \text{m} = 48.8 , \text{m} \]

  2. Calculate the total wall area (4 walls):

    \[ \text{Total wall area} = \text{Perimeter} \times \text{height} = 48.8 , \text{m} \times 4 , \text{m} = 195.2 , \text{m}^2 \]

Step 2: Calculate the area of the windows

Each window measures \(1.25 , \text{m} \times 1.8 , \text{m}\), and there are 4 windows:

\[ \text{Area of one window} = 1.25 \times 1.8 = 2.25 , \text{m}^2 \]

\[ \text{Total area of windows} = 2.25 , \text{m}^2 \times 4 = 9.0 , \text{m}^2 \]

Step 3: Calculate the area of the doors

Each door measures \(2.5 , \text{m} \times 1 , \text{m}\), and there are 2 doors:

\[ \text{Area of one door} = 2.5 \times 1 = 2.5 , \text{m}^2 \]

\[ \text{Total area of doors} = 2.5 , \text{m}^2 \times 2 = 5.0 , \text{m}^2 \]

Step 4: Calculate the total area of the windows and doors

\[ \text{Total area of windows and doors} = \text{Total area of windows} + \text{Total area of doors} = 9.0 , \text{m}^2 + 5.0 , \text{m}^2 = 14.0 , \text{m}^2 \]

Step 5: Calculate the area to be painted

\[ \text{Area to be painted} = \text{Total wall area} - \text{Total area of windows and doors} \] \[ \text{Area to be painted} = 195.2 , \text{m}^2 - 14.0 , \text{m}^2 = 181.2 , \text{m}^2 \]

Step 6: Calculate the cost to paint the walls

Given that the cost of painting is 120 shillings per square meter:

\[ \text{Cost} = \text{Area to be painted} \times \text{Cost per square meter} \] \[ \text{Cost} = 181.2 , \text{m}^2 \times 120 , \text{shillings/m}^2 = 21744 , \text{shillings} \]

Final Results

  • The area of the walls to be painted is 181.2 m².
  • The cost to paint the walls is 21,744 shillings.