Use the image to answer the question.

An illustration shows a rectangle with a length of 4 meters and a width of 3 meters.

The rectangle shows the outline of a campsite in a national forest. Anna makes a scale drawing of the campsite in which the longer side measures 1 meter. What is the area of the scale drawing in square meters?

(1 point)
Responses

12 square meters
12 square meters

0.75 square meters
0.75 square meters

3.5 square centimeters
3.5 square centimeters

1.33 square meters
1.33 square meters
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1 answer

To determine the area of the scale drawing, we first need to find the scale factor. The original rectangle has a length of 4 meters and a width of 3 meters. In Anna's scale drawing, the longer side (length) is scaled down to 1 meter.

The scale factor for the length is: \[ \text{Scale Factor} = \frac{\text{Scale Length}}{\text{Original Length}} = \frac{1 \text{ m}}{4 \text{ m}} = \frac{1}{4} \]

We will apply the same scale factor to the width to find the scale width: \[ \text{Scale Width} = \text{Original Width} \times \text{Scale Factor} = 3 \text{ m} \times \frac{1}{4} = \frac{3}{4} \text{ m} \]

Now, we calculate the area of the scale drawing: \[ \text{Area} = \text{Scale Length} \times \text{Scale Width} = 1 \text{ m} \times \frac{3}{4} \text{ m} = \frac{3}{4} \text{ square meters} = 0.75 \text{ square meters} \]

Thus, the area of the scale drawing is 0.75 square meters. The correct response is:

0.75 square meters