●=> Correct option :
![\color{plum}\tt\bold{ A = 1.69 \pi \: mm²}](https://img.qammunity.org/2022/formulas/mathematics/high-school/wfdaoq23b94cp89f0av5m5lx3mlrbxbsev.png)
●=> Steps to derive correct answer :
Given :
Circumference of a circle = 2.6π mm
We know that :
![\color{hotpink}\tt \: circumference \: of \: a \: circle\color{plum} = 2\pi r](https://img.qammunity.org/2022/formulas/mathematics/high-school/nwpzg5cyuc7cugjqf9gnpojd568nl5wn0t.png)
Which means :
![=\tt 2 * r * \pi = 2.6\pi](https://img.qammunity.org/2022/formulas/mathematics/high-school/4h8atv12f3gj0wkv0wh8mkgb03l88ez21p.png)
![=\tt r\pi = (2.6)/(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/oqyrmkyj89uygwp5lzy8t68yjqzbyt68fn.png)
![=\tt r \pi = 1.3 \: mm](https://img.qammunity.org/2022/formulas/mathematics/high-school/a0i2clrroikh6ttjk68dzr2vqygrxvvds3.png)
Thus, the radius of this circle = 1.3 mm
The area of this circle :
![=\tt \pi {r}^(2)](https://img.qammunity.org/2022/formulas/mathematics/high-school/kpdsj1bosygsnx30qy7ql0wpxmcmcmxs67.png)
![=\tt 1.3 * 1.3 * \pi](https://img.qammunity.org/2022/formulas/mathematics/high-school/qjjzwwosfekfikmvdi3yu5v73vxx1vtsnm.png)
![\color{plum} = \tt1.69\pi](https://img.qammunity.org/2022/formulas/mathematics/high-school/nyf9xi50m9umfrjwi9q3sigwmrlxjw8rdc.png)
Thus, the area of this circle = 1.69π
▪︎Therefore, the correct option is ○ A = 1.69π mm²