Area from the diagonal — Mensuration Aptitude Question
Area from the diagonal: The diagonal of a square is 8 cm. What is its area? Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Medium
- Time target: 50 seconds
Question
The diagonal of a square is 8 cm. What is its area?
Options
- 16 cm²
- 32 cm²
- 48 cm²
- 64 cm²
Show the answer and the worked solution
Correct answer: B. 32 cm²
Worked solution
- Area = d²/2 = 64/2 = 32 cm².
Answer: 32 cm².
The idea
For a square, area = d²/2 and side = d/√2. Squaring the diagonal and forgetting to halve gives 64, which is offered.
Shortcut. The diagonal splits the square into two triangles, each ½ × 8 × 4 = 16, so the area is 32.
Common trap. 16 cm² — taking the side as half the diagonal (4 cm); the side is 8 ÷ √2 ≈ 5.66 cm.