Answer:
[tex]A \approx 35.34[/tex] sq. units.
Step-by-step explanation:
A sector of a circle is a "part" of a circle.
We are given that the radius of the circle is "5" and the central angle of a sector of the circle is [tex]\frac{9}{10}\pi[/tex]
We want the area of the sector.
The angle given is in radians, so we need the formula for area of a sector of a circle (in radians), which is:
[tex]A=\frac{1}{2}r^2 \theta[/tex]
Where
r is the radius
[tex]\theta[/tex] is the angle in radians
Substituting the known values, we have:
[tex]A=\frac{1}{2}r^2 \theta\\A=\frac{1}{2}(5)^2 (\frac{9\pi}{10})\\A=\frac{1}{2}(25)(\frac{9\pi}{10})\\A=\frac{225\pi}{20}\\A=11.25\pi\\A \approx 35.34[/tex]
The area approximately is 35.34
