To determine the area of the scale drawing of the campsite, we can follow these steps:
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Calculate the area of the original rectangle:
The area \( A \) of a rectangle is calculated by the formula: \[ A = \text{length} \times \text{width} \] For the original campsite:- Length = 4 meters
- Width = 3 meters
So, \[ A = 4 , \text{meters} \times 3 , \text{meters} = 12 , \text{square meters} \]
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Find the scale factor:
In the scale drawing, the longer side (length) of the rectangle is now 1 meter. We need to find the scale factor by comparing the lengths: \[ \text{Scale factor} = \frac{\text{Length of scale drawing}}{\text{Original length}} = \frac{1 , \text{meter}}{4 , \text{meters}} = \frac{1}{4} \] -
Calculate the area of the scale drawing:
The area of a shape scales with the square of the linear dimensions. Thus, the area of the scale drawing can be calculated using the square of the scale factor: \[ \text{Area of scale drawing} = \text{Original area} \times \left(\text{Scale factor}\right)^2 \] This means: \[ \text{Area of scale drawing} = 12 , \text{square meters} \times \left(\frac{1}{4}\right)^2 = 12 , \text{square meters} \times \frac{1}{16} = \frac{12}{16} = \frac{3}{4} = 0.75 , \text{square meters} \]
Thus, the area of the scale drawing is 0.75 square meters.