Final answer:
Given the circumference of the circle is 125.6, the radius is approximately 20 units, and therefore the area is about 1256 square units.
Step-by-step explanation:
To find the area of a circle given its circumference, we first need to determine the radius of the circle. The formula for the circumference (C) of a circle is C = 2πr, where π is approximately 3.14159 and r is the radius. Given that the circumference is 125.6, we can rearrange the formula to solve for r:
r = C / (2π) = 125.6 / (2 * 3.14159) = 19.999 ≈ 20.
Now that we have the radius, we can use the formula for the area (A) of a circle, which is A = πr². Plugging in our radius we get:
A = π * (20)^2 = 3.14159 * 400 = 1256.
Therefore, the area of the circle is approximately 1256 square units. Because the radius was computed from the given circumference with only three significant figures, the final answer is reported with the same level of precision.