Count the number of triangles in the figure below.
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 6
The figure is a triangle with a line from the top corner to the middle of the base and a line joining the mid-points of the two slanting sides. A triangle is counted when all three of its sides lie on lines of the figure. Naming the corners and crossing points and counting by the number of small parts each triangle covers makes sure none is missed or counted twice.
One part (2): ABC, ACD
Two parts (3): ABD, AEF, AFG
Four parts (1): AEG
Total \(=2+3+1=6\) triangles.
Why the other options are incorrect
Option (1) 11 — Incorrect. This also counts the 5 sets of three points on one straight line, such as A, B, E, which make no triangle.
Option (2) 2 — Incorrect. This counts only the 2 smallest triangles, the ones that are a single part each.
Option (4) 5 — Incorrect. This leaves out the whole triangle AEG, which is made of four parts.