We are asked to compute the area enclosed by the curves $f(x) = \sqrt{x + 28}$ and $g(x) = \frac{1}{22}x + \frac{124}{22}$.

Steps to solve the problem:

1. Find the points of intersection: To compute the area between the curves, we need to determine where the curves intersect by solving $f(x) = g(x)$.

2. Set up the integral: The area is calculated by integrating the difference between the two functions over the interval defined by the intersection points.

Let's start by finding the intersection points between $f(x)$ and $g(x)$. We set them equal to each other:

$\sqrt{x + 28} = \frac{1}{22}x + \frac{124}{22}$

I will calculate this now.The curves $f(x) = \sqrt{x + 28}$ and ( g(x) = \frac{1}{22}x + \