How many triangles are there in the figure given below?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 8
The figure is a triangle with two lines from two corners to the middle of the opposite 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 (3): ABC, ACD, CDE
Two parts (4): ABD, ADE, AEF, BDF
Four parts (1): ADF
Total \(=3+4+1=8\) triangles.
Why the other options are incorrect
Option (1) 3 — Incorrect. This leaves out both the triangles made of four parts and those made of two parts.
Option (3) 7 — Incorrect. This leaves out the whole triangle ADF, which is made of four parts.
Option (4) 4 — Incorrect. This leaves out the 4 triangles made of two parts, such as ADE.