Question

Let P be an interior point of a convex quadrilateral ABCD and K, L, M, N be the mid-points of AB, BC, CD, DA respectively. If Area (PKAN) = 25, Area (PLBK) = 36, and Area (PMDN) = 41 then Area (PLCM) is

(a) 20

(b) 29

(c) 52

(d) 54

Answer 1

Answer is : (c) 52

Let a convex quadrilateral ABCD and K, L, M, N be the mid-point of AB, BC, CD, DA respectively.

Now, as area ∆AKP = area ∆BKP = x (let)

Similarly

It is given that Area (PKAN)