Question:
Directions: How many total number of triangles are there in the problem figure given below ?
Directions: How many total number of triangles are there in the problem figure given below ?
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The figure is symmetric: count the triangles standing on the top side, on the bottom side and on the two slanting sides, and then the large ones formed with the diagonals.
Updated On: Nov 12, 2026
- 12
- 13
- 11
- 14
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The Correct Option is A
Solution and Explanation
Let the trapezium be TL, TR (top) and BL, BR (bottom). The two diagonals meet at O. The vertical line through O meets the top side at T0 and the bottom side at B0.
Triangles with O as a vertex:
top: TL-O-T0, T0-O-TR, TL-O-TR (3)
bottom: BL-O-B0, B0-O-BR, BL-O-BR (3)
left and right slanting sides: TL-O-BL and TR-O-BR (2)
Triangles formed by the diagonals and the sides without O as a vertex: TL-BL-BR, TR-BR-BL, TL-TR-BR and TL-TR-BL (4).
Total = 3 + 3 + 2 + 4 = 12.
Answer: (1) 12
Triangles with O as a vertex:
top: TL-O-T0, T0-O-TR, TL-O-TR (3)
bottom: BL-O-B0, B0-O-BR, BL-O-BR (3)
left and right slanting sides: TL-O-BL and TR-O-BR (2)
Triangles formed by the diagonals and the sides without O as a vertex: TL-BL-BR, TR-BR-BL, TL-TR-BR and TL-TR-BL (4).
Total = 3 + 3 + 2 + 4 = 12.
Answer: (1) 12
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