To find the area of the polygon we can divide the figure into smaller figures like a rectangle and a triangle.
after we can make the mixed numbers as improper fractions to make them easier to work with
[tex]\begin{gathered} 8\frac{3}{4}=\frac{8\cdot4+3}{4}=\frac{35}{4} \\ 5\frac{1}{7}=\frac{5\cdot7+1}{4}=\frac{36}{7} \end{gathered}[/tex]
Find the area of the rectangle at the base using the formula
[tex]A=l\cdot w[/tex]
where l is b and w is a
[tex]\begin{gathered} A=\frac{36}{7}\cdot\frac{35}{4} \\ A=\frac{1260}{28} \\ A=45 \end{gathered}[/tex]
Continue by finding the area of the triangle by the formula
[tex]A=b\cdot\frac{h}{2}[/tex]
in which b is tha base b and h is the height that is represented by the difference between 10 and a.
[tex]\begin{gathered} A=(\frac{36}{7})\cdot(10-\frac{35}{4})\cdot\frac{1}{2} \\ A=(\frac{36}{7})\cdot(\frac{5}{4})\cdot\frac{1}{2} \\ A=\frac{45}{14} \\ A=3\frac{3}{14} \end{gathered}[/tex]
Add both areas together
[tex]\begin{gathered} A_p=45+3\frac{3}{14} \\ A_p=48\frac{3}{14} \end{gathered}[/tex]
