To find the area of the scale drawing of the campsite, we first need to determine the scale factor used in converting the dimensions of the rectangle from the original size to the scaled size.
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Original dimensions of the rectangle:
- Length = 4 meters
- Width = 3 meters
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Scale drawing dimensions:
- The longer side (which corresponds to the original length of 4 meters) measures 1 meter in the scale drawing.
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Calculate the scale factor: The scale factor for the length is: \[ \text{Scale factor} = \frac{\text{Length of scale drawing}}{\text{Original length}} = \frac{1 \text{ meter}}{4 \text{ meters}} = \frac{1}{4} \]
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Calculate the width of the scale drawing: To find the width of the scale drawing, we apply the same scale factor to the original width: \[ \text{Width of scale drawing} = \text{Original width} \times \text{Scale factor} = 3 \text{ meters} \times \frac{1}{4} = \frac{3}{4} \text{ meters} \]
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Calculate the area of the scale drawing: The area \( A \) of a rectangle is calculated as: \[ A = \text{Length} \times \text{Width} \] Substituting the scaled dimensions: \[ A = 1 \text{ meter} \times \frac{3}{4} \text{ meters} = \frac{3}{4} \text{ square meters} \]
To convert \( \frac{3}{4} \) square meters into decimal form, we can calculate: \[ \frac{3}{4} = 0.75 \text{ square meters} \]
Thus, the area of the scale drawing is 0.75 square meters.
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