Answer:
The area of the circle is [tex]1,215.18\ yd^{2}[/tex]
Step-by-step explanation:
we know that
The area of a circle is equal to
[tex]A=\pi r^{2}[/tex]
[tex]360\°[/tex] subtends the complete circle of area [tex]\pi r^{2}[/tex]
so
by proportion
Find the area of the complete circle if a [tex]20\°[/tex] sector has an area of [tex]21.5\pi\ yd^{2}[/tex]
[tex]\frac{x}{360}=\frac{21.5\pi}{20}\\ \\x=360*21.5\pi /20\\ \\x=387\pi \ yd^{2}[/tex]
[tex]387\pi \ yd^{2}=387*3.14=1,215.18\ yd^{2}[/tex]
