Match List I with List II. Choose the correct answer from the options given…

Area identities: a triangle's area is half its base times its height; a square's area is the square of its side; a rhombus's area is half the product of its two diagonals — valid precisely because a rhombus's diagonals bisect each other at right angles; and a parallelogram's area is the direct product of its base and height, since a parallelogram is exactly two congruent triangles of that base and height placed together.

1. Triangle Area (A) needs the identity with the factor of 1/2 applied to base and height — that is List II item III (1/2 x Base x Height).

2. Square Area (B) needs the identity for a shape whose four sides are equal and all angles are right angles — that is List II item IV, (Side)2.

3. Rhombus Area (C) needs the diagonal-based identity, because a rhombus's diagonals are always perpendicular — that is List II item II, 1/2 x (Product of diagonals).

4. Parallelogram Area (D) needs the plain base-height identity without any diagonal or halving adjustment — that is List II item I, Base x height.

Each of the four List II identities is used exactly once, and no shape is left without a match. As an independent check, a general parallelogram's diagonals need not be perpendicular, so the diagonal-based identity cannot safely be assigned to Parallelogram — confirming that identity belongs to Rhombus instead, while Parallelogram keeps the identity built purely from base and height. So the full correspondence is A - III, B - IV, C - II, D - I.