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Length and Area in Scale Drawings Quick Check
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Question
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

3.5 square centimeters
3.5 square centimeters

12 square meters
12 square meters

1.33 square meters
1.33 square meters

0.75 square meters
0.75 square meters
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Answers

Answered by GPT-4o mini
To solve for the area of Anna's scale drawing of the campsite, we start with the original dimensions of the rectangle: a length of 4 meters and a width of 3 meters.

When Anna makes a scale drawing, she sets the longer side (length) to 1 meter. To find the scale factor, we compare the lengths:

- Original length = 4 meters
- Scaled length = 1 meter
- Scale factor = (scaled length) / (original length) = 1 meter / 4 meters = 1/4

Next, we apply the same scale factor to the width:

- Original width = 3 meters
- Scaled width = 3 meters * (1/4) = 3/4 meters

Now, we calculate the area of the scale drawing:

- Area = (scaled length) * (scaled width)
- Area = (1 meter) * (3/4 meters) = 3/4 square meters

Thus, the area of the scale drawing in square meters is:

0.75 square meters

So the answer is: **0.75 square meters.**
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