Example Question - surface area for painting

Calculating Total Area for Painting Walls

The question asks which statement shows how to find the total area that the workers need to paint. The formula to calculate the area of a wall is given as Area = length x width. According to the problem, there are two sets of walls that need to be painted: - 5 walls that are 16 meters long and 4 meters high. - 6 walls that are 24 meters long and 4 meters high. Now let's calculate the area of each type of wall and then total them up: For the 5 walls that are 16 meters by 4 meters: Area for one wall = 16 x 4. Total area for these 5 walls = 5 x (16 x 4). For the 6 walls that are 24 meters by 4 meters: Area for one wall = 24 x 4. Total area for these 6 walls = 6 x (24 x 4). To get the total area to paint, we add the areas for both sets of walls: Total area = 5 x (16 x 4) + 6 x (24 x 4). Now we can look at the options provided to see which one matches our equation. Option A: \( A = 5 \cdot (16 + 4) + 6 \cdot (24 + 4) \) — This is incorrect because it improperly adds the length and width rather than multiplying them. Option B: \( A = 5 \cdot 16 + 4 + 6 \cdot 24 + 4 \) — This is incorrect because it does not group the multiplication properly and adds 4 incorrectly at the end. Option C: \( A = 5 \cdot (16 \cdot 4) + 6 \cdot (24 \cdot 4) \) — This matches our correct equation for the total area to be painted. Option D: \( A = 3 \cdot (16 \cdot 24 \cdot 4) \) — This is incorrect because it combines the numbers in a way that does not represent the problem's scenario. The correct option is therefore C: \( A = 5 \cdot (16 \cdot 4) + 6 \cdot (24 \cdot 4) \).