The area of a circle with radius r is given by the formula:
[tex]A=\pi r^2[/tex]
The circular sector is 1/4 of the whole circle. Then the area is given by 1/4 of the area of a circle:
[tex]A=\frac{1}{4}\pi r^2[/tex]
Substitute r=12 in and use 22/7 as the value for π:
[tex]\begin{gathered} A=\frac{1}{4}\times\frac{22}{7}(12in)^2 \\ =\frac{1}{4}\times\frac{22}{7}\times144in^2 \\ =\frac{3168}{28} \\ =\frac{792}{7} \\ =113.1428571\ldots \end{gathered}[/tex]
Then, the area of the shaded sector up to one decimal place is:
[tex]113.1[/tex]
