GATE EE 2023 Set 1 — Question 5
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General Aptitude → Spatial Aptitude → 2D & 3D Patterns
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Question
How many triangles are present in the given figure?
Correct answer
(C) 20
Solution
Label the outer parallelogram (with bottom-left, top-left, top-right, bottom-right) and let be the point where its diagonals and cross. The figure consists of the outer parallelogram, both diagonals and , and the inner parallelogram joining the midpoints of the four sides ( on , on , on , on ).Count triangles by size:
1.Smallest triangles: each corner triangle , , , is split by a diagonal into 2 triangles, giving .
2.Whole corner triangles: , , , , giving .
3.Triangles on a side with apex : , , , (each bounded by one side and two half-diagonals), giving .
4.Half-parallelograms cut by a diagonal: , (by ) and , (by ), giving .
The inner parallelogram's pieces are parallelograms (its sides are parallel to the diagonals), so they add no further triangles.Total .Thus, the correct option is (C).Continue learning with Success Tracker
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