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

1.33 square meters
1.33 square meters

0.75 square meters
0.75 square meters

12 square meters
12 square meters

Answer 1

To determine the area of the scale drawing of the campsite, we can follow these steps:

1. **Calculate the area of the original rectangle:**
The area \( A \) of a rectangle is calculated by the formula:
\[
A = \text{length} \times \text{width}
\]
For the original campsite:
- Length = 4 meters
- Width = 3 meters

So,
\[
A = 4 \, \text{meters} \times 3 \, \text{meters} = 12 \, \text{square meters}
\]

2. **Find the scale factor:**
In the scale drawing, the longer side (length) of the rectangle is now 1 meter. We need to find the scale factor by comparing the lengths:
\[
\text{Scale factor} = \frac{\text{Length of scale drawing}}{\text{Original length}} = \frac{1 \, \text{meter}}{4 \, \text{meters}} = \frac{1}{4}
\]

3. **Calculate the area of the scale drawing:**
The area of a shape scales with the square of the linear dimensions. Thus, the area of the scale drawing can be calculated using the square of the scale factor:
\[
\text{Area of scale drawing} = \text{Original area} \times \left(\text{Scale factor}\right)^2
\]
This means:
\[
\text{Area of scale drawing} = 12 \, \text{square meters} \times \left(\frac{1}{4}\right)^2 = 12 \, \text{square meters} \times \frac{1}{16} = \frac{12}{16} = \frac{3}{4} = 0.75 \, \text{square meters}
\]

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