How many triangles does the figure below contain?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 10
The figure is a triangle with three 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 5 points, and any 2 of these points make a triangle with A.
Triangles on one line: \(\displaystyle\frac{5\times4}{2}=10\)
On the base BF (10): ABC, ABD, ABE, ABF, ACD, ACE, ACF, ADE, ADF, AEF
Total \(=10\) triangles.
Why the other options are incorrect
Option (1) 6 — Incorrect. This leaves out the 4 triangles whose base is made of one piece.
Option (2) 8 — Incorrect. This leaves out the 2 triangles whose base is made of three pieces.
Option (4) 9 — Incorrect. This leaves out the whole triangle, whose base is made of all four pieces.