#### Answer

Area of Ring = Area of outer circle - Area of inner circle
the area of the ring = $\pi R^{2}$ - $\pi r^{2}$
= $\pi (R^{2} -r^{2})$
As we know $ (a^{2} -b^{2})$ = (a+b)(a-b)
Area of the Ring =$\pi$(R+r)(R-r)

#### Work Step by Step

Given concentric circles with radii of lengths R and r where R > r
We need to explain why
A = $\pi$(R+r)(R-r)
The area A of a circle whose radius has length r is given by
A = $\pi r^{2}$
The area of the outer circle = $\pi R^{2}$
The area of the inner circle = $\pi r^{2}$
the area of the ring = $\pi R^{2}$ - $\pi r^{2}$
= $\pi (R^{2} -r^{2})$
As we know $ (a^{2} -b^{2})$ = (a+b)(a-b)
therefore A=$\pi$(R+r)(R-r)