Count the number of triangles in the figure below.
Answer & explanation
Correct answer: option 4
The correct answer is Option (4) → 12
The figure is a rectangle with the four lines joining the mid-points of its sides and both middle lines. 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 (8): ABD, BCF, BDE, BEF, DEH, DGH, EFH, FHI
Two parts (4): BDF, BDH, BFH, DFH
Total \(=8+4=12\) triangles.
Why the other options are incorrect
Option (1) 13 — Incorrect. This counts one triangle twice; the groups above add up to 12.
Option (2) 8 — Incorrect. This leaves out the 4 triangles made of two parts, such as BFH.
Option (3) 18 — Incorrect. This also counts the 6 sets of three points on one straight line, such as A, B, C, which make no triangle.