Convert 500 cm to m. Calculate the area of one window (L=1.2m, B=0.6m). Calculate the area of the vent (diameter=0.5m, area=2pir2, pi=3.142). Calculate the area of the rectangular wall (L=5m, B=2.6m).

Here are the solutions to the questions:

1. Convert 500 cm to m.

Step 1: To convert centimeters to meters, divide by 100.

$$500 \text{ cm} = \frac{500}{100} \text{ m}$$ $$500 \text{ cm} = \boxed{\text{5 m}}$$

2. Calculate the area of one window.

Step 1: Identify the dimensions of one window from the diagram: length ($L$) = 1.2 m, breadth ($B$) = 0.6 m.

Step 2: Use the formula for the area of a rectangle, $Area = L \times B$.

$$Area_{window} = 1.2 \text{ m} \times 0.6 \text{ m}$$ $$Area_{window} = \boxed{\text{0.72 m}^2}$$

3. Calculate the area of the vent.

Step 1: Identify the diameter of the circular vent from the diagram: 0.5 m. Calculate the radius ($r$).

$$r = \frac{0.5 \text{ m}}{2} = 0.25 \text{ m}$$

Step 2: Use the given formula for the area of the vent, $Area = 2 \pi r^2$, with $\pi = 3.142$.

$$Area_{vent} = 2 \times 3.142 \times (0.25 \text{ m})^2$$ $$Area_{vent} = 2 \times 3.142 \times 0.0625 \text{ m}^2$$ $$Area_{vent} = \boxed{\text{0.39275 m}^2}$$

4. Calculate the area of the rectangular part of the wall.

Step 1: Identify the dimensions of the rectangular wall: length ($L$) = 5 m (from Q1), breadth ($B$) = 2.6 m.

Step 2: Use the formula for the area of a rectangle, $Area = L \times B$.

$$Area_{rectangular\_wall} = 5 \text{ m} \times 2.6 \text{ m}$$ $$Area_{rectangular\_wall} = \boxed{\text{13 m}^2}$$

5. Calculate the area of the gable.

Step 1: Identify the dimensions of the triangular gable: base ($b$) = 5 m, height ($h$) = 1.8 m.

Step 2: Use the formula for the area of a triangle, $Area = \frac{1}{2} \times b \times h$.

$$Area_{gable} = \frac{1}{2} \times 5 \text{ m} \times 1.8 \text{ m}$$ $$Area_{gable} = 2.5 \text{ m} \times 1.8 \text{ m}$$ $$Area_{gable} = \boxed{\text{4.5 m}^2}$$

6. Prudence states that the area of the Wall that must be painted is 14.42 m². Is this statement valid? Set your work out clearly. (PLEASE NOTE THAT THE VENT AND THE WINDOWS WILL NOT BE PAINTED)

Step 1: Calculate the total area of the front wall (rectangular part + gable).

$$Total\_wall\_area = Area_{rectangular\_wall} + Area_{gable}$$ $$Total\_wall\_area = 13 \text{ m}^2 + 4.5 \text{ m}^2$$ $$Total\_wall\_area = 17.5 \text{ m}^2$$

Step 2: Calculate the total area of the four windows.

$$Area_{4\_windows} = 4 \times Area_{window}$$ $$Area_{4\_windows} = 4 \times 0.72 \text{ m}^2$$ $$Area_{4\_windows} = 2.88 \text{ m}^2$$

Step 3: Calculate the area to be painted by subtracting the areas of the windows and the vent from the total wall area.

$$Area_{painted} = Total\_wall\_area - Area_{4\_windows} - Area_{vent}$$ $$Area_{painted} = 17.5 \text{ m}^2 - 2.88 \text{ m}^2 - 0.39275 \text{ m}^2$$ $$$$