Example 1
In given figure, ABCD is a parallelogram and EFCD is a rectangle. Also, AL ⊥ DC. Prove that
(i) ar (ABCD) = ar (EFCD)
Given that ABCD is a parallelogram
Hence AB ∥ CD
We know that a rectangle is also a parallelogram,
so EFCD is also a parallelogram
So, EF ∥ CD
Since AB ∥ CD and EF ∥ CD
we can say that EB ∥ CD
Now,
ABCD & EFDC are two parallelograms
with the same base CD
and between the same parallels EB & CD
∴ ar (ABCD) = ar (EFCD)
Example 1
In Fig., ABCD is a parallelogram and EFCD is a rectangle. Also, AL ⊥ DC. Prove that
(ii) ar (ABCD) = DC × AL
ABCD is a parallelogram with Base DC
and altitude AL
Now,
Area of a parallelogram = Base × Corresponding altitude
∴ ar (ABCD) = DC × AL
Hence proved

Davneet Singh has done his B.Tech from Indian Institute of Technology, Kanpur. He has been teaching from the past 13 years. He provides courses for Maths, Science, Social Science, Physics, Chemistry, Computer Science at Teachoo.

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