Question

ABCD is a convex quadrilateral. 3, 4, 5 and 6 points are marked on the sides AB, BC, CD and DA respectively . The number of triangles with vertices on different sides is

• A. 270
• B. 320
• C. 282
• D. 342

Answer 1

Answer: (D)

342

Answer 2

Triangles with vertices on AB, BC and CD are $3?4?5 = 60$ Triangles with vertices on AB, BC and DA are $3?4?6 = 72$ Triangles with vertices on AB, CD and DA are $3?5?6 = 90$ Triangles with vertices on BC, CDand DA are $4?5?6 = 120$ $\therefore$ Total no. of triangles $= 60 + 72 + 90 + 120 = 342$