check the picture below.
is really just 4 semi-circles and 1 square.
now, the square has sides of 4.
putting together two semi-circles, we'd get a full circle, like the ones in the picrture, therefore,
[tex]\bf \begin{array}{llll}
\textit{area of a circle}\\\\
A=\pi r^2\qquad r=radius
\end{array}\qquad \qquad
\begin{array}{llll}
\textit{area of a square}\\\\
A=s^2\qquad s=\textit{length of a side}
\end{array}\\\\
-------------------------------\\\\
\stackrel{\textit{green circle}}{\pi 2^2}+\stackrel{\textit{red circle}}{\pi 2^2}+\stackrel{square}{4^2}\implies 8\pi +16\impliedby area[/tex]
[tex]\bf \begin{array}{llll}
\textit{circumference of a circle}\\\\
A=2\pi r\qquad r=radius
\end{array}\qquad \qquad
\begin{array}{llll}
\textit{perimeter of a square}\\\\
A=4s\qquad s=\textit{length of a side}
\end{array}\\\\
-------------------------------\\\\
\stackrel{\textit{green circle}}{2\pi \cdot 2}+\stackrel{\textit{red circle}}{2\pi \cdot 2}+\stackrel{square}{4(4)}\implies 8\pi +16\impliedby perimeter[/tex]
