The area of a rhombus whose diagonals are of lengths 10 cm and 8.2 cm is

Question

The area of a rhombus whose diagonals are of lengths 10 cm and 8.2 cm is

1. A. 82 cm²
2. B. 410 cm²
3. C. 41 cm² (Correct answer)
4. D. 820 cm²

Correct Answer

Option C — 41 cm²

Detailed Solution & Explanation

The correct answer is 41 cm².

Key Points

• The area of a rhombus in terms of its diagonals $d_1$ and $d_2$ is:
  • $A = \frac{1}{2} \times d_1 \times d_2$
• Substituting $d_1 = 10$ cm and $d_2 = 8.2$ cm:
  • $A = \frac{1}{2} \times 10 \times 8.2 = 5 \times 8.2 = 41 \text{ cm}^2$

Shortcut Trick

• Halve the easier diagonal first: $10 \div 2 = 5$, then $5 \times 8.2 = 41$. Halving before multiplying avoids decimal work entirely.

Additional Information

• Why the formula works: the diagonals of a rhombus bisect each other at right angles, cutting it into four congruent right triangles of legs $\frac{d_1}{2}$ and $\frac{d_2}{2}$. Total area $= 4 \times \frac{1}{2} \times \frac{d_1}{2} \times \frac{d_2}{2} = \frac{d_1 d_2}{2}$.
• The same formula applies to any quadrilateral whose diagonals are perpendicular, including the square and the kite.
• Distractor check: 82 cm² is the product $10 \times 8.2$ with the halving forgotten — the single most common error on this question.