Question

PLEASE HELP ME .I AM CRYING. TOMORROW IS MY EXAM .
In the given figure, PQRS is a parallelogram.Points A and B trisect the base PQ.Prove that ar(ASB)=ar (ARB)=1/6 ar (PQRS).

Answer 1

Hi friend,
According to the figure:-
ar(ABS)=$\frac{1}{2}$ X AB X AS__________________(1)
and ar(PQRS)= ASX PQ_______________________________(2)
Because AS is the perpendicular height of the ||gm and also of triangle.
also AP+AB+BQ=PQ
But, AB+AB+AB=PQ( It is given that A and B trisect PQ . So, AP= AB= PQ)
3AB=PQ
and,AB=$\frac{PQ}{3}$
Now By (1)...we got,
ar(ASB)=$\frac{1}{2}$ X AB X AS
ar(ASB)=$\frac{1}{2}$ X $\frac{PQ}{3}$ X AS
ar(ASB)=$\frac{1}{6}$ X PQ X AS
ar(ASB)= $\frac{1}{6}$ X ar( PQRS) [ by (2)]
___________________________________________________thanks____