An area bounded by a 180° arc represents half the circle, as 180° is half the total circumference (360°).
Then, if the radius is 4 cm, we can caculate the green area as:
[tex]\begin{gathered} A=\frac{180}{360}A_c=\frac{1}{2}A_c=\frac{1}{2}(\pi r^2) \\ A=\frac{1}{2}\pi(4)^2 \\ A=\frac{1}{2}\pi\cdot16 \\ A=8\pi \end{gathered}[/tex]
Answer: the area is 8π square centimeters.
