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?

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.