For this case we find the area of the complete circle and then subtract the area from the circular sector, in order to have the area of the region shaded.
By definition, the area of a circle is:
[tex]A = \pi * r ^ 2[/tex]
They tell us that the radius is 8cm, then:
[tex]A = 3.14 * 8 ^ 2\\A = 3.14 * 64\\A = 200.96 \ cm ^ 2[/tex]
On the other hand, the area of the circular sector is given by:
[tex]A '= \frac {\pi * r ^ 2 * a} {360}[/tex]
We have as data that the angle of the sector is [tex]a = 135.[/tex]
[tex]A '= \frac {3.14 * 8 ^ 2 * 135} {360}\\A '= \frac {3.14 * 64 * 135} {360}\\A '= 75.36 \ cm ^ 2[/tex]
Thus, the area of the shaded region is:
[tex]A_ {sr} = 200.96 \ cm ^ 2-75.36 \ cm ^ 2\\A_ {sr} = 125.6 \ cm ^ 2[/tex]
Answer:
Option A
