The area of the shaded region is 2,674.53 square meters.
Step-by-step explanation:
Step 1:
The circumference of a circle = [tex]2\pi r[/tex] .
In the given question, the circumference of the inner circle is 122.46 meters. So we need to determine the radius of the inner circle.
[tex]2\pi r = 122.46, r = \frac{122.46}{2(3.14)} = 19.5.[/tex]
So the radius of the inner circle is 19.5 meters.
Step 2:
The radius of the outer circle = The radius of the inner circle + 15.6.
The radius of the outer circle = 19.5 + 15.6 = 35.1.
So the radius of the outer circle is 35.1 meters.
Step 3:
To calculate the area of the shaded region we subtract the area of the inner circle from the area of the outer circle.
The area of the outer circle = [tex]\pi (35.1)^{2} = 3.14 (35.1)^{2} = 3,868.5114,[/tex]
The area of the inner circle = [tex]\pi (19.5)^{2} = 3.14 (19.5)^{2} = 1.193.985.[/tex]
Step 4:
The area of the shaded region = [tex]3,868.5114 - 1,193.985 = 2,674.5264[/tex].
Rounding this off, we get the area of the shaded region is 2,674.53 square meters.
