The perimeter is the whole sides of the figure. The figure has a rectantangle and an attached semi circle.
The circumfernce of a circle is the perimeter of a circle. The circumference of a circle is
[tex]\text{circumference}=2\pi r[/tex]
Since the attached part is a semi circle the circumference will be
[tex]\begin{gathered} \text{circumference}=\frac{1}{2}\times2\pi r \\ \text{circumference}=\pi r \\ r=\frac{8}{2}=4 \\ \text{circumference}=4\pi \end{gathered}[/tex]
perimeter of the figure is therefore,
[tex]\begin{gathered} \text{perimeter}=8+10+10+4\pi \\ \text{perimeter}=28+4\pi \\ \text{perimeter}=28+\frac{4\times22}{7} \\ \text{perimeter}=28+\frac{88}{7} \\ \text{perimeter}=28+12.5714285714 \\ \text{perimeter}=40.5714285714 \\ \text{perimeter}\approx40.6 \end{gathered}[/tex]
