Use the image to answer the question.

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

1.33 square meters
1.33 square meters

12 square meters
12 square meters

0.75 square meters

Answer 1

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) is represented as 1 meter.

1. Determine the scale factor:

   • Original length: 4 meters
   • Scale length: 1 meter
   • Scale factor = Scale length / Original length = 1 meter / 4 meters = 1/4

2. Determine the dimensions of the scale drawing:

   • Original width: 3 meters
   • Scale width = Original width × Scale factor = 3 meters × (1/4) = 3/4 meters

Now, we can find the area of the scale drawing:

3. Calculate area of the scale drawing:
   • Area = Length × Width = (1 meter) × (3/4 meters) = 3/4 square meters

Converting \(3/4\) to decimal gives us \(0.75\) square meters.

Thus, the area of the scale drawing is:

0.75 square meters.