Answer:
[tex]192.27\:\mathrm{cm^2}[/tex]
Step-by-step explanation:
The area of sector with radius [tex]r[/tex] and measure [tex]\theta[/tex] is give by [tex]A=r^2\pi\cdot \frac{\theta}{360^{\circ}}[/tex]. Since vertical angles are congruent, the two shaded sectors in the figure are congruent.
What we're given:
- 2 sectors of equal area
- Each sector has a radius of 9 cm
- Each sector has a measure of 136 degrees
Therefore, the area of the shaded regions (two sectors) is:
[tex]A=2\cdot 9^2\pi\cdot \frac{136}{360}=192.2654704\approx \boxed{192.27\:\mathrm{cm^2}}[/tex]
