Question

Abcd is a parallelogram and t is the mid point of ad. If at of quadrilateral abct = 45 sq units , then find area of triangle tcd.

Answer 1

ABCD is a parallelogram, with the base as AD (for example).
T is midpoint of AD.  
Let  E be the midpoint of BC.  Join TE and TC.

Let the Area of ΔCTD = x sq units.
We know that TECD is also a parallelogram with area = 1/2 of ABCD.

Ar(TECD) = ΔTEC + ΔTCD = 2 * Δ TCD   (In this parallelogram, TC is the diagonal. So the area of both triangles is the same).

Hence Ar(ABCD) = 4 * ΔTCD
    Also  Ar(quadrilateral  ABCT) = 45 sq units
             Ar(ABCT) + ΔTEC = 3 * ΔTCD
             ΔTCD = 15 sq units.