To find the area of a circle given its circumference, you can use the following steps:

Step 1: Recall the formulas

• The formula for the circumference of a circle is: $C = 2\pi r$ where $r$ is the radius of the circle.

• The formula for the area of a circle is: $A = \pi r^2$

Step 2: Find the radius

Given the circumference $C = 19\pi$ meters, you can solve for the radius $r$: $2\pi r = 19\pi$ Now, divide both sides by $2\pi$ to solve for $r$: $r = \frac{19\pi}{2\pi} = \frac{19}{2} = 9.5 \text{ meters}$

Step 3: Calculate the area

Now that we have the radius, we can find the area $A$: $A = \pi r^2 = \pi (9.5)^2$ $A = \pi \times 90.25 = 90.25\pi \text{ square meters}$

So, the area of the circle is 90.25π square meters.

Would you like more details or have any questions?

Here are some related questions you might find interesting:

1. What would the area be if the circumference were doubled?
2. How does the area change if the radius is doubled?
3. What is the diameter of the circle?
4. How would the area change if the circumference were 10π meters?
5. How do you calculate the area if the diameter is given instead of the circumference?

Tip: The relationship between circumference and radius is key to finding the area when you don't have the radius directly.