To determine the area of Alfredo’s scale drawing, we first need to know the dimensions of the original poster and the scale he used to create the smaller version.
Since the information about the original dimensions and the scale factor isn't provided in your question, let me illustrate how you would calculate the area provided you have that information.
-
Identify the Dimensions of the Original Poster: Let's say the original poster has a length of \(L\) meters and a width of \(W\) meters.
-
Determine the Scale Factor: If Alfredo makes a smaller version, we need to know the scale factor. For example, if Alfredo scales down the top edge to \(L' = \frac{1}{2}L\) (this is just an example scale factor).
-
Calculate the New Dimensions: If the original width is \(W\), the new width would also be scaled down accordingly (the same scale factor applies).
- \(W' = \text{scale factor} \times W\)
-
Calculate the Area of the Scale Drawing:
- Area = Length × Width
- For the scale drawing, the area would be: \(A' = L' \times W' = \left(\text{scale factor} \times L\right) \times \left(\text{scale factor} \times W\right) = \text{scale factor}^2 \times (L \times W)\)
-
Convert Units (if necessary): Make sure both dimensions are in the same unit (like inches or meters) when calculating the area.
Assuming we did have the dimensions and the scale, you'd substitute those values in to find the area. Based on the options you provided, we need to evaluate the possible areas.
If you could provide the original dimensions of the poster and the scale ratio used by Alfredo, I could help you calculate the exact area for his scale drawing. Otherwise, from the options given (13 sq meters, 1/3 sq meters, 12 sq inches, 96 sq inches, 192 sq inches), you can compare which could be the likely area of a scaled-down version based on reasonable scaling from standard poster dimensions.
If you need to make an estimation without these details, typically posters might be 24"x36" or some standard size, and the scaled version could likely be one of the given areas, depending on the scale factor used.