Answer:
[tex]40\pi \ m^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
In this problem we have
[tex]r=10\ m[/tex]
Substitute and find the area
[tex]A=\pi (10)^{2}=100 \pi\ m^{2}[/tex]
Remember that
[tex]360\°[/tex] subtends the area of complete circle
so
by proportion
Find the area of the shaded regions
The central angle of the shaded regions is equal to [tex]2*72\°=144\°[/tex]
[tex]\frac{100\pi }{360} \frac{m^{2}}{degrees} =\frac{x }{144} \frac{m^{2}}{degrees} \\ \\x=144*100\pi /360\\ \\ x=40\pi \ m^{2}[/tex]
