Sure! Let's solve this step-by-step:
1. Understand the Scale:
- According to the problem, 1 millimeter in the drawing represents 150 meters in real life.
2. Determine the Scale Conversion for Area:
- Since 1 millimeter on the drawing represents 150 meters in real life, we need to find out how many square millimeters on the drawing represent 1 square meter in real life.
- Recall that area scales by the square of the linear scale factor:
[tex]\[
\text{Scale Factor} = 150
\][/tex]
Thus:
[tex]\[
(\text{Scale Factor})^2 = 150^2 = 22,500
\][/tex]
3. Calculate the Representation of 1 Square Meter:
- If 1 millimeter represents 150 meters, then:
[tex]\[
1 \text{ square meter} = \left(\frac{1}{150}\right)^2 \text{ square millimeters}
\][/tex]
[tex]\[
\left(\frac{1}{150}\right)^2 = \frac{1^2}{150^2} = \frac{1}{22,500}
\][/tex]
4. Answer:
- Therefore, 1 square meter is represented by [tex]\(\frac{1}{22,500}\)[/tex] square millimeters on the drawing.
Thus, the correct answer is [tex]\( \boxed{\frac{1}{22,500}} \)[/tex].
