●=> Correct option :
[tex]\color{plum}\tt\bold{ A = 1.69 \pi \: mm²}[/tex]
●=> Steps to derive correct answer :
Given :
Circumference of a circle = 2.6π mm
We know that :
[tex]\color{hotpink}\tt \: circumference \: of \: a \: circle\color{plum} = 2\pi r[/tex]
Which means :
[tex] =\tt 2 \times r \times \pi = 2.6\pi[/tex]
[tex] =\tt r\pi = \frac{2.6}{2} [/tex]
[tex] =\tt r \pi = 1.3 \: mm[/tex]
Thus, the radius of this circle = 1.3 mm
The area of this circle :
[tex] =\tt \pi {r}^{2} [/tex]
[tex] =\tt 1.3 \times 1.3 \times \pi[/tex]
[tex]\color{plum} = \tt1.69\pi[/tex]
Thus, the area of this circle = 1.69π
▪︎Therefore, the correct option is ○ A = 1.69π mm²
