Find the total number of triangles in the given figure.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 9
The figure is a triangle with one line from the top corner and two lines across it. Every triangle in it has the top corner A as one corner and its base on one of the lines across, the base included. On each such line the lines from A meet 3 points, and any 2 of these points make a triangle with A.
Triangles on one line: \(\displaystyle\frac{3\times2}{2}=3\)
On BD (3): ABC, ABD, ACD
On EG (3): AEF, AEG, AFG
On the base HJ (3): AHI, AHJ, AIJ
Total \(=3\times3=9\) triangles.
Why the other options are incorrect
Option (2) 6 — Incorrect. This leaves out the 3 triangles standing on the base.
Option (3) 10 — Incorrect. This counts one triangle twice; the lines give exactly 9.
Option (4) 3 — Incorrect. This counts only the 3 triangles standing on the base.