We have the following:
[tex]p=2\cdot l+2\cdot w[/tex]
Where p is perimeter, l is the length and w is the width, replacing:
[tex]\begin{gathered} l=4\cdot w+6 \\ p=92 \\ 92=2\cdot(4\cdot w+6)+2\cdot w \\ 92=6w+12+2w \\ 8w=92-12 \\ w=\frac{80}{8} \\ w=8 \end{gathered}[/tex]
for the length:
[tex]\begin{gathered} l=4\cdot8+6 \\ l=38 \end{gathered}[/tex]
Now, the area is:
[tex]\begin{gathered} A=l\cdot w \\ A=8\cdot38 \\ A=304 \end{gathered}[/tex]
The anwers is 304 square meters
