The diagonals of a rhombus are 64 cm and 96 cm, respectively. The area of the…

Concept: For a rhombus, the two diagonals bisect each other at right angles, splitting the rhombus into four congruent right triangles. This gives the identity Area = (1/2) × d1 × d2, where d1 and d2 are the lengths of the two diagonals.

Application: Substitute the given diagonal lengths into the identity:

1. Identify the diagonals: d1 = 64 cm and d2 = 96 cm.

2. Write the formula with these values: Area = (1/2) × 64 × 96.

3. Compute the product of the diagonals: 64 × 96 = 6144.

4. Halve the product: 6144 ÷ 2 = 3072.

Cross-check: Each diagonal is bisected into two equal halves — 32 cm (half of 64 cm) and 48 cm (half of 96 cm) — which are the legs of each of the four right triangles formed. Area of one triangle = (1/2) × 32 × 48 = 768 cm2. Four such triangles give 4 × 768 = 3072 cm2, which matches the result above.

Result: The area of the rhombus is 3072 cm2.