first off, the area will be the product of the length and width, in this case 1/3 and 3 and 5/8.
now, let's convert the mixed fraction to "improper", and then get that product,
[tex]\bf \stackrel{mixed}{3\frac{5}{8}}\implies \cfrac{3\cdot 8+5}{8}\implies \stackrel{improper}{\cfrac{29}{8}}
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\cfrac{1}{3}\cdot \cfrac{29}{8}\implies \cfrac{29}{24}\implies 1\frac{5}{24}[/tex]