How many triangles are there in the figure given below?
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 12
The figure is a triangle with lines from the two base corners to the middle of the opposite sides and a line joining the mid-points of the two slanting sides. 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
Three parts (2): ABF, ACE
Five parts (1): AEF
Total \(=5+4+2+1=12\) triangles.
Why the other options are incorrect
Option (1) 9 — Incorrect. This counts only the triangles made of one and of two parts.
Option (2) 5 — Incorrect. This counts only the 5 smallest triangles, the ones that are a single part each.
Option (3) 8 — Incorrect. This leaves out the 4 triangles made of two parts, such as CEF.