To find the area of the scale drawing, we first need to determine the scale factor used in Anna's drawing. The original rectangle has a length of 4 meters and a width of 3 meters. In the scale drawing, the longer side (length) measures 1 meter.
Calculating the scale factor:
- Original length = 4 meters
- Scale drawing length = 1 meter
The scale factor is:
\[ \text{Scale Factor} = \frac{\text{Scale Drawing Length}}{\text{Original Length}} = \frac{1 \text{ meter}}{4 \text{ meters}} = \frac{1}{4} \]
Now, we apply the same scale factor to find the width in the scale drawing:
- Original width = 3 meters
Using the scale factor:
\[ \text{Scale Drawing Width} = \frac{\text{Original Width}}{4} = \frac{3 \text{ meters}}{4} = 0.75 \text{ meters} \]
Now we calculate the area of the scale drawing:
\[ \text{Area of Scale Drawing} = \text{Scale Drawing Length} \times \text{Scale Drawing Width} = 1 \text{ meter} \times 0.75 \text{ meters} = 0.75 \text{ square meters} \]
Thus, the area of the scale drawing is 0.75 square meters.