Respuesta :

we'll first convert the mixed fractions to "improper" and then get their product, since the area of a rectangle is the product of its length and width.

[tex]\bf \stackrel{mixed}{5\frac{1}{6}}\implies \cfrac{5\cdot 6+1}{6}\implies \stackrel{improper}{\cfrac{31}{6}} \\\\\\ \stackrel{mixed}{2\frac{2}{7}}\implies \cfrac{2\cdot 7+2}{7}\implies \stackrel{improper}{\cfrac{16}{7}} \\\\\\ \cfrac{31}{6}\cdot \cfrac{16}{7}\implies \cfrac{496}{42}\implies \stackrel{simplified}{\cfrac{248}{21}}\implies 11\frac{17}{21}[/tex]

Area of the rectangle in mixed fraction is

[tex]11\frac{17}{21} \; \; cm^2[/tex]

Given :

From the given figure , the length of the rectangle is [tex]5\frac{1}{6} cm[/tex]

Width of the rectangle is [tex]2\frac{2}{7}[/tex]

Now we find out the area of the rectangle using formula

[tex]Area = length \cdot width[/tex]

First we convert mixed fractions into improper fractions

[tex]5\frac{1}{6} =\frac{5 \cdot 6+1}{6} =\frac{31}{6}[/tex]

[tex]2\frac{2}{7}=\frac{2 \cdot 7+2}{7} =\frac{16}{7}[/tex]

Now we find out the area

[tex]Area = length \cdot width\\Area =\frac{31}{6} \cdot \frac{16}{7} \\Area =\frac{496}{42} \\Simplify \; it \\Area =\frac{248}{21}=11\frac{17}{21}[/tex]

Area of the rectangle is [tex]11\frac{17}{21} \; \; cm^2[/tex]

Learn more :  brainly.com/question/10299654

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