How many triangles are there in the figure given below?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 9
The figure is an envelope: a rectangle with both diagonals and a triangle on top. A triangle is counted when all three of its sides lie on lines of the figure. Naming the corners and crossing points and counting by the number of small parts each triangle covers makes sure none is missed or counted twice.
One part (5): ABC, BCD, BDE, CDF, DEF
Two parts (4): BCE, BCF, BEF, CEF
Total \(=5+4=9\) triangles.
Why the other options are incorrect
Option (2) 11 — Incorrect. This also counts the 2 sets of three points on one straight line, such as B, D, F, which make no triangle.
Option (3) 10 — Incorrect. This counts one triangle twice; the groups above add up to 9.
Option (4) 5 — Incorrect. This leaves out the 4 triangles made of two parts, such as BCF.