Find the total number of triangles in the given figure.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 11
The figure is a square with one diagonal and two lines from a corner to the middle of the far 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): ABD, ADG, DFG, EFH, FGH
Two parts (4): ABG, AFG, DGH, EGH
Three parts (2): ACH, AGH
Total \(=5+4+2=11\) triangles.
Why the other options are incorrect
Option (1) 5 — Incorrect. This counts only the 5 smallest triangles, the ones that are a single part each.
Option (2) 9 — Incorrect. This counts only the triangles made of one and of two parts.
Option (3) 7 — Incorrect. This leaves out the 4 triangles made of two parts, such as ABG.