To determine the area of the scale drawing, we first need to establish the scale based on the given dimensions of the rectangle and the scale drawing.
The original rectangle has:
- Length = 4 meters
- Width = 3 meters
The area of the original rectangle is: \[ \text{Area} = \text{Length} \times \text{Width} = 4 , \text{meters} \times 3 , \text{meters} = 12 , \text{square meters} \]
Anna’s scale drawing has the longer side measuring 1 meter.
To find the scale factor:
- Original length (4 meters) corresponds to the scale drawing length (1 meter).
- Thus, the scale factor is: \[ \text{Scale factor} = \frac{1 , \text{meter}}{4 , \text{meters}} = \frac{1}{4} \]
Now, we apply the scale factor to the width:
- Original width = 3 meters.
- The scaled width will be: \[ \text{Scaled width} = 3 , \text{meters} \times \frac{1}{4} = 0.75 , \text{meters} \]
Now we can find the area of the scale drawing: \[ \text{Area of the scale drawing} = \text{Scaled Length} \times \text{Scaled Width} = 1 , \text{meter} \times 0.75 , \text{meters} = 0.75 , \text{square meters} \]
Therefore, the area of the scale drawing is 0.75 square meters.
The correct response is: 0.75 square meters.