Find the total number of triangles in the given figure.
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 6
The figure is a triangle with two 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 4 points, and any 2 of these points make a triangle with A.
Triangles on one line: \(\displaystyle\frac{4\times3}{2}=6\)
On the base BE (6): ABC, ABD, ABE, ACD, ACE, ADE
Total \(=6\) triangles.
Why the other options are incorrect
Option (2) 5 — Incorrect. This leaves out the whole triangle, whose base is made of all three pieces.
Option (3) 4 — Incorrect. This leaves out the 2 triangles whose base is made of two pieces.
Option (4) 3 — Incorrect. This leaves out the 3 triangles whose base is made of one piece.