How many triangles are there in the figure given below?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 16
The figure is a square with both diagonals and both middle lines. 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 (8): ABE, ADE, BCE, CEF, DEG, EFI, EGH, EHI
Two parts (4): ACE, AEG, CEI, EGI
Four parts (4): ACG, ACI, AGI, CGI
Total \(=8+4+4=16\) triangles.
Why the other options are incorrect
Option (2) 17 — Incorrect. This counts one triangle twice; the groups above add up to 16.
Option (3) 12 — Incorrect. This leaves out the 4 triangles made of two parts, such as ACE.
Option (4) 8 — Incorrect. This leaves out both the triangles made of four parts and those made of two parts.