Count the number of triangles in the figure below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 16
The figure is a triangle with a line from each corner to the middle of the opposite side. 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 (6): ABD, ACD, BDE, CDG, DEF, DFG
Two parts (3): ADE, ADG, DEG
Three parts (6): ABG, ACE, AEF, AFG, BEG, CEG
Six parts (1): AEG
Total \(=6+3+6+1=16\) triangles.
Why the other options are incorrect
Option (1) 15 — Incorrect. This leaves out the whole triangle AEG, which is made of six parts.
Option (2) 10 — Incorrect. This leaves out the 6 triangles made of three parts, such as AEF.
Option (4) 13 — Incorrect. This leaves out the 3 triangles made of two parts, such as ADE.