Given:
Area of a circle = 254.34 mm^2
Let's find the diameter.
First Step: Use the formula for area of a circle to find the radius of the circle.

where
Area = 254.34
r = radius
π = 3.14
Let's find the radius:
Rewrite the formula for r
![\begin{gathered} A\text{ = }\pi r^2 \\ \\ r=\sqrt[]{(A)/(\pi)} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/w2ht3td3li8v34kapywz7jbyoc14ysea3e.png)
![\begin{gathered} r\text{ = }\sqrt[]{(254.34)/(3.14)} \\ \\ \text{ =}\sqrt[]{81}=\text{ 9} \end{gathered}](https://img.qammunity.org/2023/formulas/mathematics/college/bqfvut39rhpejvd5h2p19koszlw96vnn2a.png)
Radius of the circle = 9 mm
We know that diameter = radius x 2
Therefore
diameter of the circle = 9 x 2 = 18 mm
ANSWER:
diameter = 18 mm