How many triangles does the figure below contain?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 16
The figure is a rectangle made of two squares, each with one diagonal, and one long diagonal of the rectangle. 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): AEF, BCD, CDG, CGH, DEG, EFG
Two parts (6): ABG, ACE, AFG, BCG, CEG, DFG
Three parts (2): ACF, CFG
Four parts (2): ACG, CFH
Total \(=6+6+2+2=16\) triangles.
Why the other options are incorrect
Option (1) 14 — Incorrect. This leaves out the 2 triangles made of three parts, such as ACF.
Option (2) 6 — Incorrect. This counts only the 6 smallest triangles, the ones that are a single part each.
Option (4) 10 — Incorrect. This leaves out the 6 triangles made of two parts, such as ACE.