Answer:
0.67 cm^2
Explanation:
The angle subtended by the shaded region is 360 - 240 = 120 degrees.
Therefore, the shaded region represents
[tex]\frac{120}{360}=\frac{1}{3}[/tex]
of the whole circle.
Now, the area of the whole circle is
[tex]A=\pi r^2[/tex]
In our case, the radius is 0.8 cm; therefore,
[tex]A=\pi\times(0.8)^2[/tex][tex]A=0.64\pi[/tex][tex]\Rightarrow A=2.012[/tex]
The area of the shaded portion is 1/3 of the area of the whole circle. Therefore,
[tex]A_{\text{shaded}}=\frac{1}{3}\times2.012[/tex][tex]\boxed{A_{\text{shaded}}=0.67\; cm^2\text{.}}[/tex]
Hence, the area of the shaded portion is sqaure centimetres.
