The problem asks to evaluate the expression $(74.3 \text{ m} - 23.8 \text{ dm}) \cdot (970 \text{ cm} - 31 \text{ dm}) + 3.8 \text{ m} \cdot 96 \text{ dm}$. The answer should be in square meters.

1. Problem Description

The problem asks to evaluate the expression $(74.3 \text{ m} - 23.8 \text{ dm}) \cdot (970 \text{ cm} - 31 \text{ dm}) + 3.8 \text{ m} \cdot 96 \text{ dm}$. The answer should be in square meters.

2. Solution Steps

First, we convert all measurements to meters:

$1 \text{ dm} = 0.1 \text{ m}$

$1 \text{ cm} = 0.01 \text{ m}$

So we have:

$23.8 \text{ dm} = 23.8 \cdot 0.1 \text{ m} = 2.38 \text{ m}$

$970 \text{ cm} = 970 \cdot 0.01 \text{ m} = 9.7 \text{ m}$

$31 \text{ dm} = 31 \cdot 0.1 \text{ m} = 3.1 \text{ m}$

$96 \text{ dm} = 96 \cdot 0.1 \text{ m} = 9.6 \text{ m}$

Now, we substitute these values into the expression:

$(74.3 \text{ m} - 2.38 \text{ m}) \cdot (9.7 \text{ m} - 3.1 \text{ m}) + 3.8 \text{ m} \cdot 9.6 \text{ m}$

$= (71.92 \text{ m}) \cdot (6.6 \text{ m}) + 3.8 \text{ m} \cdot 9.6 \text{ m}$

$= 474.672 \text{ m}^2 + 36.48 \text{ m}^2$

$= 511.152 \text{ m}^2$

3. Final Answer

$511.152 \text{ m}^2$