Area of the shaded figure is,
[tex]\text{Area = }277cm^2[/tex]
The given shaded region represents the sector of a circle . The central angle covered by the given region is,
[tex]\begin{gathered} \text{Central angle = 360 - 72} \\ \text{Central angle = 288} \end{gathered}[/tex]
Area of a sector is given as,
[tex]\begin{gathered} \text{Area of sector = }\frac{\theta}{360}\text{ }\times\text{ }\pi\times r^2 \\ 277\text{ = }\frac{288}{360}\text{ }\times\text{ }3.14\text{ }\times r^2 \\ \end{gathered}[/tex]
The radius of the circle G is calculated as,
[tex]\begin{gathered} r^2\text{ = }\frac{277\times360}{288\times3.14} \\ r^2\text{ = }\frac{99720}{904.32} \\ r^2\text{ = }110.27 \\ r\text{ = 10.5 } \end{gathered}[/tex]
The diameter of the circle G is calculated as,
[tex]\begin{gathered} \text{Diameter = 2r} \\ \text{Diameter = 2 }\times\text{ 10.5} \\ \text{Diameter = 21 }cm \end{gathered}[/tex]
Thus the diameter of the given circle is 21 cm.
