The given problem is an analogy question involving geometric shapes. Let's analyze the pattern:

1. The first figure in the analogy is a triangle within a square.
2. The second figure shows that a smaller shape (a square) has been added inside the triangle, maintaining the outer square boundary.

We need to apply a similar transformation to the third figure (an inverted triangle within a square) to find the analogous fourth figure.

1. Observe the transformation from the first figure to the second one: a square is added inside the triangle.
2. Applying the same logic to the inverted triangle, we should add a similar smaller square inside it.

The option that matches this transformation is the one where a smaller square is added inside the inverted triangle, keeping the outer square boundary intact.

Thus, the correct answer is the fourth option.