Mathematics
In the figure (1) given, ABCD and AEFG are two parallelograms. Prove that area of || gm ABCD = area of || gm AEFG.
Theorems on Area
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Answer
(a) Join BG.
We know that,
Since, ∆ABG and || gm ABCD lie on same base AB and between same parallel lines AB and CD.
Area of ∆ABG = Area of ||gm ABCD ……(i)
Since, ∆ABG and || gm AEFG lie on same base AG and between same parallel lines AG and EF.
Area of ∆ABG = Area of ||gm AEFG ……(ii)
From (i) and (ii) we get,
Area of || gm ABCD = Area of || gm AEFG
⇒ Area of || gm ABCD = Area of || gm AEFG
Hence, proved that area of || gm ABCD = area of || gm AEFG.
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