To find the area of the rectangle (campsite) in the scale drawing where the longer side measures 1 meter, we first need to determine the scale factor based on the dimensions provided (height of 4 m and width of 3 m).
Here, the longer side of the rectangle (height) is 4 meters, and the shorter side (width) is 3 meters. Since the longer side is being scaled down to 1 meter in the drawing, we need to calculate the corresponding measurement for the width.
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Determine the scale factor: \[ \text{Scale factor} = \frac{\text{Length of longer side in drawing}}{\text{Actual length of longer side}} = \frac{1 \text{ m}}{4 \text{ m}} = \frac{1}{4} \]
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Calculate the width in the scale drawing: Since the width is 3 m in reality, we apply the scale factor to find the width in the drawing. \[ \text{Width in drawing} = 3 \text{ m} \times \frac{1}{4} = \frac{3}{4} \text{ m} = 0.75 \text{ m} \]
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Calculate the area of the scale drawing: Now that we have the dimensions of the scale drawing (1 meter by 0.75 meters), we find the area: \[ \text{Area} = \text{Length} \times \text{Width} = 1 \text{ m} \times 0.75 \text{ m} = 0.75 \text{ m}^2 \]
Therefore, the area of the scale drawing in square meters is: \[ \boxed{0.75} \]