Find the total number of triangles in the given figure.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 20
The figure is a triangle with three lines from the top corner and one line 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 5 points, and any 2 of these points make a triangle with A.
Triangles on one line: \(\displaystyle\frac{5\times4}{2}=10\)
On BC (10): ABC, ABD, ABE, ABF, ACD, ACE, ACF, ADE, ADF, AEF
On the base GK (10): AGH, AGI, AGJ, AGK, AHI, AHJ, AHK, AIJ, AIK, AJK
Total \(=10\times2=20\) triangles.
Why the other options are incorrect
Option (1) 8 — Incorrect. This counts only the 8 smallest triangles, whose base is a single piece.
Option (2) 14 — Incorrect. This leaves out the 6 triangles whose base is made of two pieces.
Option (3) 18 — Incorrect. This leaves out the 2 triangles whose base is made of four pieces.