To determine the area of the scale drawing of the campsite, we need to first calculate the area of the original rectangle and then apply the scale to find the area of the scaled version.
The area of the original rectangle can be calculated using the formula for the area of a rectangle:
\[ \text{Area} = \text{length} \times \text{width} \]
For the original campsite:
- Length = 4 meters
- Width = 3 meters
Calculating the area:
\[ \text{Area} = 4 , \text{meters} \times 3 , \text{meters} = 12 , \text{square meters} \]
Now, in the scale drawing, the longer side (length) of the rectangle measures 1 meter instead of 4 meters. To find the scale factor, we compare the scaled length to the original length:
\[ \text{Scale Factor} = \frac{1 , \text{meter}}{4 , \text{meters}} = \frac{1}{4} \]
This means that both dimensions of the rectangle in the scale drawing will be \(\frac{1}{4}\) of the original dimensions. So the width in the scale drawing will be:
\[ \text{Scaled Width} = \frac{3}{4} , \text{meters} \]
Now we can find the area of the scale drawing:
\[ \text{Scaled Area} = \text{Scaled Length} \times \text{Scaled Width} = 1 , \text{meter} \times \frac{3}{4} , \text{meters} = \frac{3}{4} , \text{square meters} = 0.75 , \text{square meters} \]
Thus, the area of the scale drawing is 0.75 square meters.
The correct response is:
0.75 square meters.