To find the area of Alfredo's scale drawing, we first need to determine the dimensions of the original poster based on the information provided in the table.
The original poster has these dimensions:
- Left edge: 36 inches
- Top edge: 24 inches
The area of a rectangle is calculated using the formula: \[ \text{Area} = \text{Length} \times \text{Width} \]
Substituting the dimensions of the original poster into the formula: \[ \text{Area} = 36 , \text{inches} \times 24 , \text{inches} = 864 , \text{square inches} \]
Now, we need to find the dimensions of Alfredo's scale drawing. The problem states that he makes a scale drawing with the length of the top edge as mentioned in the table (which is given as 8 inches). In this case, we will assume that the scale ratio is the same for both dimensions.
To find the scaling factor, we see that the original top edge is 24 inches and the scale drawing's top edge is 8 inches: \[ \text{Scale factor} = \frac{8}{24} = \frac{1}{3} \]
Now, we can find the new dimensions of the scale drawing:
- New left edge (scaled down from 36 inches): \[ \text{New left edge} = 36 \times \frac{1}{3} = 12 , \text{inches} \]
Now we have the dimensions of Alfredo’s scale drawing:
- Left edge: 12 inches
- Top edge: 8 inches
Finally, we can calculate the area of the scale drawing: \[ \text{Area} = \text{Length} \times \text{Width} \] \[ \text{Area} = 12 , \text{inches} \times 8 , \text{inches} = 96 , \text{square inches} \]
Thus, the area of Alfredo’s scale drawing is 96 square inches.