Find how many triangles are there in the given figure?
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 12
To count triangles without missing any, letter every point where lines meet and count by the number of small parts a triangle covers. The line from B through E to F is one straight line, so B, E and F never form a triangle.
The figure is cut into five small triangles: ABE, AEF, BDE, DCE and ECF.
Triangles of one part: ABE, AEF, BDE, DCE, ECF — 5
Triangles of two parts: ABF (ABE + AEF), ABD (ABE + BDE), AEC (AEF + ECF), BEC (BDE + DCE) — 4
Triangles of three parts: ADC (AEF + ECF + DCE), BFC (BDE + DCE + ECF) — 2
The whole triangle ABC — 1
Total \(=5+4+2+1=\) 12 triangles.