Mathematics
In figure (3) given below, AB || DC || EF, AD || BE and DE || AF. Prove that the area of DEFH is equal to the area of ABCD.
Theorems on Area
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Answer
We know that,
AD || BE ⇒ AD || EG
ED || FA ⇒ ED || GA
Since, opposite sides are parallel.
Hence, ADEG is a parallelogram.
Since || gm ABCD and || gm ADEG lie on same base AD and between same parallel lines AD and EB,
area of || gm ABCD = area of ||gm ADEG ……. (i)
We know that,
ED || FA ⇒ DE || FH
DH || EF
Since, opposite sides are parallel.
Hence, DEFH is a parallelogram.
Since || gm DEFH and || gm ADEG lie on same base DE and between same parallel lines DE and FA,
area of ||gm DEFH = area of ||gm ADEG ……. (ii)
From (i) and (ii) we get,
⇒ area of ||gm ABCD = area of ||gm DEFH
Hence, proved that area of ||gm ABCD = area of ||gm DEFH.
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