# Chapter 1 - Section 1.9 - Distance and Midpoint Formulas; Circles - Exercise Set - Page 282: 96

$11\pi$

#### Work Step by Step

Step 1. We can identify the first equation as a circle centered at $(2,-3)$, with a radius $r_1=5$ Step 2. We can identify the second equation as a circle centered at $(2,-3)$, with a radius $r_2=6$ Step 3. The area of the donut-shaped region can be found as $\Delta A=\pi r_2^2-\pi r_1^2=\pi (6^2-5^2)=11\pi$

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