Answer
$1.92$ square inches
Work Step by Step
The area of a sector can be computed using the formula:
$K=\frac{\theta}{360}\cdot \pi \cdot r^2$,where $\theta$ is in degrees
Hence, here we have
$K_1=\frac{50}{360}\cdot \pi \cdot 6^2\approx15.71.$
By definition the area of a triangle is given by the formula:
$K_2=\frac{ab\cdot \sin(C)}{2}.$
Hence, here we have
$K_2=\frac{6\cdot6\cdot \sin(50^o)}{2}\approx13.79.$
Thus, the area of the segment is:
$K_1-K_2=15.71-13.79=1.92$
