The problem provided is based on the Pythagorean Theorem and involves algebraic manipulation to isolate $a^2$. Let's break it down step by step:

1. Starting Equation: $a^2 + b^2 = c^2$ From the diagram, we know that:

   • $b = 2$ (the length of the other leg),
   • $c = 4$ (the hypotenuse).

2. Substitute the values: $a^2 + 2^2 = 4^2$ This simplifies to: $a^2 + 4 = 16$

3. Subtract 4 from both sides: $a^2 = 16 - 4$ $a^2 = 12$

So, the value remaining for $a^2$ is 12.

Would you like further details on this solution or have any additional questions?

Here are 5 related questions you might find useful:

1. How do you solve for $a$ after finding $a^2 = 12$?
2. Can the Pythagorean Theorem be used for non-right triangles?
3. What are the conditions under which the Pythagorean Theorem holds true?
4. How would this problem change if one of the other triangle sides was unknown?
5. How does the Pythagorean Theorem relate to the distance formula in coordinate geometry?

Tip: Always remember that the Pythagorean Theorem applies only to right triangles. It’s a great tool for solving geometric problems involving distances and angles.