To find the area of the scale drawing of the campsite, we first need to identify the dimensions of the actual campsite based on the given information.
The height and width of the campsite are given as follows:
- Height: 4 meters
- Width: 3 meters
To calculate the area of the actual campsite, we use the formula for the area of a rectangle:
\[ \text{Area} = \text{Height} \times \text{Width} \]
Substituting the values we have:
\[ \text{Area} = 4 , \text{m} \times 3 , \text{m} = 12 , \text{m}^2 \]
Next, we need to confirm the scale of the drawing. We understand that in the scale drawing, the longer side (which is the height of 4 meters) is represented as 1 meter.
To find the scale, we determine the ratio of the heights:
\[ \text{Scale ratio} = \frac{\text{Length in drawing}}{\text{Actual length}} = \frac{1 , \text{m}}{4 , \text{m}} = \frac{1}{4} \]
Now we can scale down the width accordingly. The actual width is 3 meters, so in the scale drawing, the width will also be reduced by the same scale factor:
\[ \text{Width in drawing} = 3 , \text{m} \times \frac{1}{4} = \frac{3}{4} , \text{m} \]
Now that we have the dimensions of the scale drawing:
- Height in drawing: 1 meter
- Width in drawing: \( \frac{3}{4} , \text{m} \)
We can now compute the area of the scale drawing:
\[ \text{Area} = \text{Height in drawing} \times \text{Width in drawing} \]
Substituting the values:
\[ \text{Area} = 1 , \text{m} \times \frac{3}{4} , \text{m} = \frac{3}{4} , \text{m}^2 \]
Thus, the area of the scale drawing in square meters is:
\[ \boxed{\frac{3}{4}} , \text{m}^2 \]