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

0.75 square meters
0.75 square meters

3.5 square centimeters
3.5 square centimeters

12 square meters
12 square meters

1.33 square meters
1.33 square meters
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1 answer

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

Calculating the scale factor:

  • Original length = 4 meters
  • Scale drawing length = 1 meter

The scale factor is:

\[ \text{Scale Factor} = \frac{\text{Scale Drawing Length}}{\text{Original Length}} = \frac{1 \text{ meter}}{4 \text{ meters}} = \frac{1}{4} \]

Now, we apply the same scale factor to find the width in the scale drawing:

  • Original width = 3 meters

Using the scale factor:

\[ \text{Scale Drawing Width} = \frac{\text{Original Width}}{4} = \frac{3 \text{ meters}}{4} = 0.75 \text{ meters} \]

Now we calculate the area of the scale drawing:

\[ \text{Area of Scale Drawing} = \text{Scale Drawing Length} \times \text{Scale Drawing Width} = 1 \text{ meter} \times 0.75 \text{ meters} = 0.75 \text{ square meters} \]

Thus, the area of the scale drawing is 0.75 square meters.