Correct option: (d) 342
Explanation:
Number of triangles with vertices on AB, BC, CD = 3C1 × 4C1 × 5C1
with vertices on sides AB, BC, DA = 3C1 × 4C1 × 6C1
with vertices on sides AB, CD, DA = 3C1 × 5C1 × 6C1
with vertices on sides BC, CD, DA = 4C1 × 4C1 × 6C1
Total triangles = (3C1 × 4C1 × 5C1) + (3C1 × 4C1 × 6C1) + (3C1 × 5C1 × 6C1) + (4C1 × 5C1 × 6C1)
= (3 × 4 × 5) + (3 × 4 × 6) + (3 × 5 × 6) + (4 × 5 × 6)
= 342