Concentric Circles:
Concentric circles are circles that share the same center point but have different radii. The radii of the circles gradually increase or decrease as we move from the innermost circle to the outermost circle.

Finding the Area of Outer and Inner Circles:
To find the area of a circle, we use the formula A = πr², where A is the area and r is the radius of the circle. Since we have concentric circles, we will have two circles - an outer circle and an inner circle.

1. Outer Circle:
Let's assume that the radius of the outer circle is R. Using the formula, the area of the outer circle is A = πR².

2. Inner Circle:
Let's assume that the radius of the inner circle is r. Using the formula, the area of the inner circle is A = πr².

Finding the Area of the Middle Region:
To find the area of the middle region, we need to subtract the area of the inner circle from the area of the outer circle.

1. Area of the Middle Region:
The area of the middle region can be calculated as:
Middle Region Area = Area of Outer Circle - Area of Inner Circle
Middle Region Area = πR² - πr²

Verifying Using π(R - r)(R + r):
We can verify the result using the formula π(R - r)(R + r), which gives the same result as the difference between the areas of the outer and inner circles.

1. Verifying:
π(R - r)(R + r) = π(R² - r²)
= πR² - πr²

This confirms that the formula π(R - r)(R + r) is equivalent to the difference between the areas of the outer and inner circles, which is the area of the middle region.

In conclusion, to find the area of concentric circles, we calculate the areas of the outer and inner circles using the formula A = πr², and then find the area of the middle region by subtracting the area of the inner circle from the area of the outer circle. This can also be verified using the formula π(R - r)(R + r), which gives the same result.