The diagonals of a rhombus are 65 cm and 56 cm respectively. Find the area of…

Concept: The area of a rhombus is half the product of its diagonals, because the diagonals of a rhombus bisect each other at right angles and divide it into four congruent right triangles whose combined area equals (d1 × d2) / 2.

Application: For this rhombus:

1. The two diagonals are d1 = 65 cm and d2 = 56 cm.

2. Multiply the diagonals: 65 × 56 = 3640.

3. Divide by 2 to get the area: 3640 ÷ 2 = 1820 cm2.

Cross-check: 65 × 56 can be split as (65 × 50) + (65 × 6) = 3250 + 390 = 3640, confirming the product; halving it independently, 3640 ÷ 2 = 1820, matches the direct calculation, so the working is consistent.

Result: The area of the rhombus is 1820 cm2.