We need to find the value of the expression $(12.4 + 8.2)^2$.

1. Problem Description

We need to find the value of the expression $(12.4 + 8.2)^2$.

2. Solution Steps

First, we need to evaluate the expression inside the parentheses:

$12.4 + 8.2 = 20.6$

Next, we need to square the result:

$(20.6)^2 = 20.6 \times 20.6$

To calculate $20.6 \times 20.6$, we can perform the multiplication:

$20.6 \times 20.6 = 424.36$

3. Final Answer

The value of $(12.4 + 8.2)^2$ is $424.36$.