Question

Pqrs is a parallelogram and x and y trisect side qr Show that area of ar triangle pqx is equal to ar sry

Answer 1

PQRS is a parallelogram, we know PQ= RS and PQ || RS and QR = SP and QR || SP and X and Y trisect the side QR, the diagram which will be formed is attached: 

QX =XY = RY --- (1)

we know, the area of triangle = 1/2 x base x height

and height of both triangle PQX and SRY is = h, as (these triangles are lies between same parallel lines QR || SP)

SO,

Area of triangle PQX = 1/2 x QX x h ---- (2)
and 
Area of triangle SRY = 1/2 x RY x h  we will substitute the values from equation 1 and will get the area of triangle SRY = 1/2 x QX x h --- (3)

from equation 2 and 3 we will get the area of  triangle PQX  = area of triangle SRY