ABCD is a rectangle with 'o' as any point in its interior if area of triangle AOD=3cm square and - Maths - Areas of Parallelograms and Triangles

Question

ABCD is a rectangle with 'o' as any point in its interior if
area of triangle AOD=3cm square and area triangle BOC= 6cm square
then find the area of rectangle ABCD

Ajanta Trivedi · Accepted Answer

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.

$\frac{1}{2} * A D * O E + \frac{1}{2} * O F * B C = 9 \frac{1}{2} [A D * O E + O F * B C] = 9 A D * O E + O F * A D = 9 * 2 = 18$ since BC=AD [opposite sides of a rectangle]

$\Rightarrow A D (O E + O F) = 18 A D * E F = 18$ since EF=AB

AD*AB=18

area of the rectangle ABCD = AB*AD=18

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ABCD is a rectangle with 'o' as any point in its interior. if area of triangle AOD=3cm square and area triangle BOC= 6cm square then find the area of rectangle ABCD.