How many triangles does the figure below contain?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 15
The figure is a triangle with four lines from the top corner to the base. Every triangle in it has the top corner A as one corner and its base on the base. On the base the lines from A meet 6 points, and any 2 of these points make a triangle with A.
Triangles on one line: \(\displaystyle\frac{6\times5}{2}=15\)
On the base BG (15): ABC, ABD, ABE, ABF, ABG, ACD, ACE, ACF, ACG, ADE, ADF, ADG, AEF, AEG, AFG
Total \(=15\) triangles.
Why the other options are incorrect
Option (2) 13 — Incorrect. This leaves out the 2 triangles whose base is made of four pieces.
Option (3) 5 — Incorrect. This counts only the 5 smallest triangles, whose base is a single piece.
Option (4) 14 — Incorrect. This leaves out the whole triangle, whose base is made of all five pieces.