How many triangles are there in the given figure?
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → 28
Name the points as in the figure below and count square by square, then the triangles that spread over two squares.
Inside one square (ABFE):
The diagonals cut it into 4 small triangles: APB, BPF, FPE, EPA
Each diagonal also cuts it into two halves: ABF, AEF (by AF) and ABE, BEF (by BE), 4 more
So each square has 8 triangles, and the three squares have \(3\times8=24\)
Across two squares (two diagonals that meet at a corner, with the top or bottom line as base):
ACF and BDG, with bases on the top line
EGB and FHC, with bases on the bottom line
Total \(=24+4=28\).