Answer
$0.69$ square inches
Work Step by Step
The Area of sector can be computed by:
$K=\frac{\theta}{360}\cdot \pi \cdot r^2$,where $\theta$ is in degrees
Hence, the area of the sector is
$K_1=\frac{40}{360}\cdot \pi \cdot 5^2\approx8.73$ square inches
By definition the area of a triangle is given by the formula:
$K_2=\frac{ab\cdot \sin(C)}{2}$
Hence the area of the triangle is
$K=\frac{5\cdot5\cdot \sin(40^o)}{2}\approx8.04$ square inches
Thus, the area of the segment:
$K_1-K_2=8.73-8.04=0.69$ square inches
