Solve the following math problem efficiently and clearly:

- For simple problems (2 steps or fewer):
Provide a concise solution with minimal explanation.

- For complex problems (3 steps or more):
Use this step-by-step format:

## Step 1: [Concise description]
[Brief explanation and calculations]

## Step 2: [Concise description]
[Brief explanation and calculations]

...

Regardless of the approach, always conclude with:

Therefore, the final answer is: $oxed{answer}$. I hope it is correct.

Where [answer] is just the final number or expression that solves the problem.

Problem: In the figure below, a 3-inch by 3-inch square adjoins a 10-inch by 10-inch square. What is the area of the shaded region? Express your answer in square inches as a common fraction. [asy]
unitsize(2mm);
defaultpen(linewidth(0.7pt)+fontsize(12pt));

pair H=(0,0), A=(0,10), B=(10,10), C=(10,3), G=(10,0), E=(13,3), F=(13,0);
pair D=extension(A,F,B,G);

draw(A--B--G--H--cycle);
fill(D--C--E--F--cycle, black);
draw(A--F);
draw(G--F--E--C);

label("$A$",A,NW);
label("$H$",H,SW);
label("$B$",B,NE);
label("$C$",C,NE);
label("$G$",G,S);
label("$D$",D,WSW);
label("$E$",E,NE);
label("$F$",F,SE);
[/asy]
user