The lengths of the diagonals of a rhombus are 8 cm and 6 cm. Using the standard diagonal-based formula, what is the area of this rhombus in square centimetres?

Introduction / Context:
Rhombus area problems test whether you know the important formula that links the area of a rhombus to the lengths of its diagonals. This formula is especially useful when side length is not given but diagonals are provided, as in many aptitude and geometry questions.

Given Data / Assumptions:

• The figure is a rhombus.
• Length of the first diagonal d1 = 8 cm.
• Length of the second diagonal d2 = 6 cm.
• We are asked for the area in cm².
• Diagonals of a rhombus intersect at right angles and bisect each other.

Concept / Approach:
The area A of a rhombus in terms of its diagonals d1 and d2 is given by: A = (1/2) * d1 * d2 This comes from the fact that the diagonals divide the rhombus into four congruent right triangles, each with legs equal to half of the diagonals.

Step-by-Step Solution:
Given d1 = 8 cm and d2 = 6 cm. Use the formula A = (1/2) * d1 * d2. Substitute: A = (1/2) * 8 * 6. Compute 8 * 6 = 48. Then A = (1/2) * 48 = 24 cm2.

Verification / Alternative check:
Each right triangle formed by the diagonals has legs 4 cm and 3 cm (half of 8 and 6). The area of one right triangle is (1/2) * 4 * 3 = 6 cm2. There are four such triangles, so total area = 4 * 6 = 24 cm2, which matches our previous calculation.

Why Other Options Are Wrong:
48 cm2 is the product d1 * d2 without multiplying by 1/2, so it is exactly double the correct area. 60 cm2 and 96 cm2 are even larger and have no basis in the standard rhombus area formula for these diagonal lengths.

Common Pitfalls:
A classic error is forgetting the factor of 1/2 and writing A = d1 * d2. Another pitfall is confusing side length with diagonal length; the usual parallelogram formula base * height is not directly usable without extra information, so the diagonal-based formula is the most efficient approach here.

Final Answer:
The area of the rhombus is 24 cm2.