How many triangles does the figure below contain?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 5
The figure is a rectangle made of two squares with two slanting lines that meet at the middle of the base. 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 (4): ABE, ADE, BCE, CEF
Two parts (1): ACE
Total \(=4+1=5\) triangles.
Why the other options are incorrect
Option (2) 7 — Incorrect. This also counts the 2 sets of three points on one straight line, such as A, B, C, which make no triangle.
Option (3) 4 — Incorrect. This counts only the 4 smallest triangles, the ones that are a single part each.
Option (4) 6 — Incorrect. This counts one triangle twice; the groups above add up to 5.