https://file.aiquickdraw.com/mathbot/file/1730144278280pwshne1k.jpg

To solve for the area of the real backyard, we need to understand the scaling and calculate the dimensions in real measurements.

### Step-by-Step Solution

1. **Identify the scale**: According to the problem, **2 cm in the drawing represents 3 m in real life**.

2. **Calculate the real dimensions of the backyard**:
   - In the drawing, the **width** of the backyard is 2 cm.
     - Using the scale, this becomes:
       \[
       \text{Real width} = \frac{2 \text{ cm} \times 3 \text{ m}}{2 \text{ cm}} = 3 \text{ m}
       \]
   - The **height** of the backyard in the drawing is 4 cm.
     - Using the scale, this becomes:
       \[
       \text{Real height} = \frac{4 \text{ cm} \times 3 \text{ m}}{2 \text{ cm}} = 6 \text{ m}
       \]

3. **Calculate the area of the real backyard**:
   - Area = Real width \(\times\) Real height
   \[
   \text{Area} = 3 \text{ m} \times 6 \text{ m} = 18 \text{ m}^2
   \]

### Answer
The area of the real backyard is **18 m²**.

Would you like further details, or do you have any questions?

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Here are five related questions to expand on this topic:

1. How would the area change if the backyard width in the drawing was increased to 3 cm?
2. What would the area be if the drawing scale changed to 1 cm representing 1 m?
3. How do we calculate area when the shape is not rectangular?
4. How can we apply similar scaling techniques in real-world engineering problems?
5. How would the calculations change if we measured in feet instead of meters?

**Tip:** When using scale drawings, always double-check that all measurements are converted properly based on the given scale.

A scale drawing for a plot of land is shown below. In the drawing, 2 cm represents 3 m. Assuming the backyard is rectangular, find the area of the real backyard.

This lesson explains how to calculate the real area of a rectangular backyard using a scale drawing. It covers ratios and proportions, area calculation formulas, and using the given scale of 2 cm to 3 m. Suitable for Grades 6-8.

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