Area by Heron's formula — Mensuration Aptitude Question
Area by Heron's formula: What is the area of a triangle with sides 13 cm, 14 cm and 15 cm? Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Hard
- Time target: 120 seconds
Question
What is the area of a triangle with sides 13 cm, 14 cm and 15 cm?
Options
- 78 cm²
- 84 cm²
- 91 cm²
- 96 cm²
Show the answer and the worked solution
Correct answer: B. 84 cm²
Worked solution
- s = (13 + 14 + 15)/2 = 21.
- Area = √(21 × (21−13) × (21−14) × (21−15)) = √(21 × 8 × 7 × 6).
- = √7056 = 84 cm².
Answer: 84 cm².
The idea
Heron's formula when no height is given. The 13-14-15 triangle with area 84 is a standard exam favourite, so it is worth recognising on sight.
Shortcut. Split the 14 cm side as 5 + 9: the 5-12-13 and 9-12-15 right triangles share a height of 12, so the area is ½ × 14 × 12 = 84.
Common trap. 91 cm² — treating 13 and 14 as the legs of a right triangle (½ × 13 × 14); the triangle is not right-angled.