The formula for the area of a sector is given as
[tex]\begin{gathered} \text{Area of a sector=}\frac{\theta}{360}\times\pi r^2 \\ \text{where,} \\ \theta=\sec toralangle=72^0 \\ r=\text{radius}=4\operatorname{cm} \end{gathered}[/tex]
By substitution,
[tex]\begin{gathered} \text{Area of sector= }\frac{72^0}{360^0}\times\pi\times(4\operatorname{cm})^2 \\ \text{Area of sector=}\frac{\text{72}\times\pi\times16\operatorname{cm}^2}{360} \\ \text{Area of sector}=\frac{1152\pi\operatorname{cm}^2}{360} \\ \text{Area of sector}=10.053\operatorname{cm}^2 \end{gathered}[/tex]
Hence,
The area of the sector=10.053 square centimeters
