Answer:
![A=15\pi\ units^2](https://tex.z-dn.net/?f=A%3D15%5Cpi%5C%20units%5E2)
Step-by-step explanation:
<u><em>The picture of the question in the attached figure</em></u>
we know that
It is given that the diameter of 5 circles making up the archery is 2,4,6,8, and 10.
To determine the total red area, we use the formula for area of the circle
![A=\pi r^{2}](https://tex.z-dn.net/?f=A%3D%5Cpi%20r%5E%7B2%7D)
step 1
Find the Area of the 1st red circle
---> the radius is half the diameter
![A_1=\pi (1)^{2}=\pi\ units^2](https://tex.z-dn.net/?f=A_1%3D%5Cpi%20%281%29%5E%7B2%7D%3D%5Cpi%5C%20units%5E2)
step 2
Find the Area of the 2nd white circle
---> the radius is half the diameter
![A_2=\pi (2)^{2}=4\pi\ units^2](https://tex.z-dn.net/?f=A_2%3D%5Cpi%20%282%29%5E%7B2%7D%3D4%5Cpi%5C%20units%5E2)
step 3
Find the Area of the 3rd red circle
---> the radius is half the diameter
![A_3=\pi (3)^{2}=9\pi\ units^2](https://tex.z-dn.net/?f=A_3%3D%5Cpi%20%283%29%5E%7B2%7D%3D9%5Cpi%5C%20units%5E2)
step 4
Find the Area of the 4th white circle
---> the radius is half the diameter
![A_4=\pi (4)^{2}=16\pi\ units^2](https://tex.z-dn.net/?f=A_4%3D%5Cpi%20%284%29%5E%7B2%7D%3D16%5Cpi%5C%20units%5E2)
step 5
Find the Area of the 5th red circle
---> the radius is half the diameter
![A_5=\pi (5)^{2}=25\pi\ units^2](https://tex.z-dn.net/?f=A_5%3D%5Cpi%20%285%29%5E%7B2%7D%3D25%5Cpi%5C%20units%5E2)
The total red area is given by
![A=A_5-A_4+A_3-A_2+A_1](https://tex.z-dn.net/?f=A%3DA_5-A_4%2BA_3-A_2%2BA_1)
substitute
![A=25\pi-16\pi+9\pi-4\pi+\pi](https://tex.z-dn.net/?f=A%3D25%5Cpi-16%5Cpi%2B9%5Cpi-4%5Cpi%2B%5Cpi)
![A=15\pi\ units^2](https://tex.z-dn.net/?f=A%3D15%5Cpi%5C%20units%5E2)