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 answer

To determine the area of the scale drawing, we first need to establish the scale based on the given dimensions of the rectangle and the scale drawing.

The original rectangle has:

  • Length = 4 meters
  • Width = 3 meters

The area of the original rectangle is: \[ \text{Area} = \text{Length} \times \text{Width} = 4 , \text{meters} \times 3 , \text{meters} = 12 , \text{square meters} \]

Anna’s scale drawing has the longer side measuring 1 meter.

To find the scale factor:

  • Original length (4 meters) corresponds to the scale drawing length (1 meter).
  • Thus, the scale factor is: \[ \text{Scale factor} = \frac{1 , \text{meter}}{4 , \text{meters}} = \frac{1}{4} \]

Now, we apply the scale factor to the width:

  • Original width = 3 meters.
  • The scaled width will be: \[ \text{Scaled width} = 3 , \text{meters} \times \frac{1}{4} = 0.75 , \text{meters} \]

Now we can find the area of the scale drawing: \[ \text{Area of the scale drawing} = \text{Scaled Length} \times \text{Scaled Width} = 1 , \text{meter} \times 0.75 , \text{meters} = 0.75 , \text{square meters} \]

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

The correct response is: 0.75 square meters.