Question

A flagpole stands on a concrete region, as shown.

Answer 1

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,

$\bf \begin{array}{llll} \textit{area of a circle}\\\\ A=\pi r^2\qquad r=radius \end{array}\qquad \qquad \begin{array}{llll} \textit{area of a square}\\\\ A=s^2\qquad s=\textit{length of a side} \end{array}\\\\ -------------------------------\\\\ \stackrel{\textit{green circle}}{\pi 2^2}+\stackrel{\textit{red circle}}{\pi 2^2}+\stackrel{square}{4^2}\implies 8\pi +16\impliedby area$



$\bf \begin{array}{llll} \textit{circumference of a circle}\\\\ A=2\pi r\qquad r=radius \end{array}\qquad \qquad \begin{array}{llll} \textit{perimeter of a square}\\\\ A=4s\qquad s=\textit{length of a side} \end{array}\\\\ -------------------------------\\\\ \stackrel{\textit{green circle}}{2\pi \cdot 2}+\stackrel{\textit{red circle}}{2\pi \cdot 2}+\stackrel{square}{4(4)}\implies 8\pi +16\impliedby perimeter$