Question

PQRS is a rectangle with O as any point in its interior. If area (ΔPOS)=4 sq cm and area(ΔQOR)= 6 sq cm, then area of rectangle ​

Answer 1

Step-by-step explanation:

given: ABCD is a rectangle, and O is any point in its interior.

area(ΔAOD)= 3 sqcm and area(ΔBOC)=6 sq cm.

from O draw a line EF parallel to AB intersecting AD at E and BC at F.

therefore OE⊥AD and OF⊥BC.

let OE=x and OF=y

OE+OF=EF=AB

therefore x+y=AB......(1)

area(ΔAOD)+area(ΔBOC)=3+6=9 sq cm.

since BC=AD [opposite sides of a rectangle]

since EF=AB

AD*AB=18

area of the rectangle ABCD = AB*AD=18