The perimeter of a rectangle is calculated using the formula:
[tex]P=2(l+w)[/tex]The question gives that the length and width of the rectangle are equal. This means that:
[tex]l=w[/tex]Therefore, the perimeter will be calculated to be:
[tex]\begin{gathered} P=2(l+l)=2(2l) \\ P=4l \end{gathered}[/tex]The perimeter is given to be 32 m. Therefore, the length of the rectangle will be:
[tex]\begin{gathered} 32=4l \\ l=\frac{32}{4} \\ l=8 \end{gathered}[/tex]Using the formula for the area:
[tex]A=l^2[/tex]Therefore, the area will be:
[tex]\begin{gathered} A=8^2 \\ A=64\text{ m}^2 \end{gathered}[/tex]The area is 64 square meters.