The answer is 37.68
We need to find the area of the sector of the circle.
There is a missing part in the upper left part of the circle.
The upper left part central angle measure 90 degree becuase it has a perpendicular sign.
Using central angle and arc theorem, the central angle equal the arc measure so that arc measure is 90 degrees.
There is 360 degrees in a circle so using arc addition,
the rest of the arc measure 270 degrees.
We can use this formula to find the area of the sector
[tex] \frac{x}{360} \times \pi \times {r}^{2} [/tex]
where x is the measure of the central angle and r is the radius.
Plug 270 in for x. The radius is 4.
[tex] \frac{270}{360 } \times \pi \times {4}^{2} [/tex]
[tex] \frac{3}{4} \times \pi \times 16[/tex]
[tex]12\pi[/tex]
which is about
37.68
