(x-5)² + (y-4.5)² = 1  what is the area

The given equation is in the form of a **circle equation**: 

\[
(x - h)^2 + (y - k)^2 = r^2
\]

Where:
- \((h, k)\) is the center of the circle, and 
- \(r\) is the radius.

In your case:
- Center: \((5, 4.5)\),
- Radius \(r = 1\) (since \(r^2 = 1\)).

The area \(A\) of a circle is given by the formula:

\[
A = \pi r^2
\]

Since \(r = 1\):

\[
A = \pi \times 1^2 = \pi
\]

Thus, the area of the circle is \(\pi\) square units.

Would you like more details on circle equations or related concepts?

Here are some related questions:
1. How would the area change if the radius was doubled?
2. What is the circumference of this circle?
3. How can we find the equation of a circle from three points?
4. What is the general formula for the equation of a circle in polar coordinates?
5. How do you calculate the distance between two points on the circumference?

**Tip:** In circle geometry, knowing the radius allows you to quickly compute both area and circumference, making it a critical piece of information!

Learn how to find the area of a circle from its equation (x-5)² + (y-4.5)² = 1. This problem covers important geometry concepts, including the standard form of a circle equation and the formula for calculating area. Suitable for students in Grades 8-10.

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