How many triangles are there in the following figure?
Answer & explanation
Correct answer: option 3
The correct answer is Option (3) → 18
The figure is a rectangle made of two squares, ABEF and BCDE, with both diagonals drawn in each square. The triangles are counted square by square, and then the ones that cross the middle line BE.
In the square ABEF: 8 triangles
4 small triangles round the centre O: AOB, BOE, EOF, FOA
4 halves of the square cut off by a diagonal: ABE, AEF, ABF, BEF
In the square BCDE: 8 triangles in the same way
4 small triangles round the centre P: BPC, CPD, DPE, EPB
4 halves: BCD, BDE, BCE, CDE
Across BE: AC and FD are single straight lines, so ACE and BFD are triangles too, 2 more
Total: \(8+8+2=18\)