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------------------------------------------------ Convert and simplify the expression:

Multiply [tex]$5.9 \, \text{dm}$[/tex] and [tex]$35.8 \, \text{cm}$[/tex] by a certain number [tex]$a \, \text{m}$[/tex].

Answer :

We start by converting both measurements to meters.

Step 1. Convert decimeters to meters:
Since [tex]\(1\,\text{dm} = 0.1\,\text{m}\)[/tex], then
[tex]\[
5.9\,\text{dm} = 5.9 \times 0.1\,\text{m} = 0.59\,\text{m}.
\][/tex]

Step 2. Convert centimeters to meters:
Since [tex]\(1\,\text{cm} = 0.01\,\text{m}\)[/tex], then
[tex]\[
35.8\,\text{cm} = 35.8 \times 0.01\,\text{m} = 0.358\,\text{m}.
\][/tex]

Step 3. Multiply the converted lengths:
To find the area in square meters, multiply the two converted values (note that [tex]\( \text{m} \times \text{m} = \text{m}^2 \)[/tex]):
[tex]\[
\text{Area} = 0.59\,\text{m} \times 0.358\,\text{m} = 0.21122\,\text{m}^2.
\][/tex]

Thus, the final answer is
[tex]\[
\boxed{0.21122\,\text{m}^2}.
\][/tex]