1. Given the area \(A = 113 \space \text { cm} ^ 2\) and \(\pi = 3.14\).
2. Use the area formula \(A = \pi r^ 2\):
   \[113 = 3.14 r^ 2\]
3. Solve for \(r^ 2\):
   \[r^ 2 = \frac { 113} { 3.14} \approx 36\]
4. Find \(r\):
   \[r = \sqrt { 36} \approx 6\]
5. Use the circumference formula \(C = 2 \pi r\):
   \[C = 2 \times 3.14 \times 6 \approx 37.68\]

Round to the nearest tenth:
\[C \approx 37.6\]
 

Supplemental Knowledge

To find the circumference of a circle when you know its area, you need to use the relationship between the area and the radius of the circle. The formulas involved are:

The area of a circle: \(A = \pi r^ 2\)

The circumference of a circle: \(C = 2 \pi r\)
Given the area, you can solve for the radius (\(r\)) and then use that radius to find the circumference.
 

Knowledge in Action

Knowing how to calculate properties of circles can come in handy in various real-life applications, like designing or installing a round garden or swimming pool. Knowing measurements such as area and circumference helps estimate materials required and costs involved for such endeavors.

Mastering geometric concepts like calculating areas and circumferences can significantly enhance your problem-solving skills! For more practice with geometry or other math topics such as algebra or trigonometry, explore UpStudy’s live tutor question bank or AI-powered problem-solving services! Visit UpStudy today and elevate your learning experience with personalized support tailored just for you!