Answer:
The area is equal to
![5.29 \pi\ m^(2)](https://img.qammunity.org/2020/formulas/mathematics/high-school/bqrdg4s3fxqd9zxyv3vxqm1ddlf0xwocbu.png)
Explanation:
Step 1
Find the radius r
we know that
the circumference of a circle is equal to
![C=2\pi r](https://img.qammunity.org/2020/formulas/mathematics/middle-school/kmguleyi3d7rsbh4zj0jg7p7fumid62phf.png)
In this problem we have
![C=4.6 \pi\ m](https://img.qammunity.org/2020/formulas/mathematics/high-school/frwjw71kyt2hgh8fkt6rv4h42yyyqjan9j.png)
Substitute in the formula and solve for r
![4.6 \pi=2\pi r](https://img.qammunity.org/2020/formulas/mathematics/high-school/656erxwvdtr8b0cv751xcapxmtu5f2jn7l.png)
![r=4.6/2=2.3\ m](https://img.qammunity.org/2020/formulas/mathematics/high-school/hjrmlzi6v9wjzwbp3hrikrk8719wv8zvhx.png)
Step 2
Find the area
we know that
The area of a circle is equal to
![A=\pi r^(2)](https://img.qammunity.org/2020/formulas/mathematics/middle-school/2z11w6ajg8k9itft7shcdqinea4lmf008k.png)
substitute the value of r
![A=\pi (2.3^(2))=5.29 \pi\ m^(2)](https://img.qammunity.org/2020/formulas/mathematics/high-school/rjwhr69v78cqqgkqhzsnjryl3p0h2k7jyc.png)