Question

PQRS is a //gm Amd X and Y trisect sides OR. Show that ar( triangle PQS) =ar( triangleSRY).

Answer 1

solution:-

here, it is given :- PQRS is a parallelogram ,

So we know PQ = RS and PQ | | RS and QR = SP and QR | | SP

And
X and Y trisect the side QR , So

QX = XY = RY --------------------【 1 】

We know , Area of triangle = 1/2×Base×Height

And Height of both triangle PQX and SRY is = h , As ( These triangle are lies between same parallel lines QR | | SP )

SO,

Area of ∆ PQX = 12QX × h......................【 2 】

And
Area of ∆ SRY = 12RY × h ,
Substitute values from equation 1 and get

Area of ∆ SRY = 12QX × h.....................【 3 】

From equation【 2】 and【 3 】, we get

Area of PQX = Area of SRY ( Hence proved )...............................【 ANS】