The following figure shows a triangle ABC in which P, Q and R are mid-points of sides AB, BC and CA respectively. S is mid-point of PQ. Prove that :

ar.(△ ABC) = 8 × ar.(△ QSB)

In the given figure, the diagonals AC and BD intersect at point O. If OB = OD and AB // DC, prove that :

(i) Area of (△ DOC) = Area of (△ AOB)

(ii) Area of (△ DCB) = Area of (△ ACB)

(iii) ABCD is a parallelogram.

In △ ABC, E and F are mid-points of sides AB and AC respectively. If BF and CE intersect each other at point O, prove that the △ OBC and quadrilateral AEOF are equal in area.

In parallelogram ABCD, P is mid-point of AB. CP and BD intersect each other at point O. If area of △ POB = 40 cm² and OP : OC = 1 : 2, find :

(i) Areas of △ BOC and △ PBC

(ii) Area of △ ABC and parallelogram ABCD.