Area of a 5–12–13 triangle — Mensuration Aptitude Question
Area of a 5–12–13 triangle: What is the area of a triangle with sides 5 cm, 12 cm and 13 cm? Answer and worked solution on CodeKairo.
- Topic: Mensuration
- Section: Quantitative Aptitude
- Difficulty: Easy
- Time target: 40 seconds
Question
What is the area of a triangle with sides 5 cm, 12 cm and 13 cm?
Options
- 30 cm²
- 32.5 cm²
- 60 cm²
- 65 cm²
Show the answer and the worked solution
Correct answer: A. 30 cm²
Worked solution
- 25 + 144 = 169 = 13², so the triangle is right-angled with legs 5 and 12.
- Area = ½ × 5 × 12 = 30 cm².
Answer: 30 cm².
The idea
Recognise Pythagorean triples (3-4-5, 5-12-13, 8-15-17, 7-24-25) and skip Heron's formula entirely.
Shortcut. 5-12-13 is right-angled, so area = ½ × 5 × 12 = 30 and the hypotenuse never enters; options built on 13, like 32.5 = ½ × 5 × 13, are out.
Common trap. 60 cm² — multiplying the legs and forgetting the ½; the rectangle 5 × 12 is twice the triangle.