In fig, PQRS and ABRS are parallelograms and X is any point on side BR. Show that (i) area(PQRS) = area(ABRS) (ii) area(AXS) = 1/2 area(PQRS)

(i) For parallelogram PQRS and ABRS, we notice that they lie on the same base RS and between the same parallel lines RS and PB. So, area(PQRS) = area(ABRS). (1) (since parallelograms lying on the same base RS and between the same parallel lines have equal area)
(ii) For △AXS and parallelogram ABRS, we notice that they lie on the same base SA and between the same parallel lines SA and BR. So, area(△AXS) = 1/2 area(ABRS). (2) (since parallelogram and triangle lying on the same base and between the same parallel lines have equal area)
Substituting equation (1) in equation (2), we get area(△AXS) = 1/2 area(PQRS)