If ABCD and EFGH are two parallelograms between the same parallel lines and on the same base, then:

We know that the Area of a parallelogram is given by the formula = base ⨯ height

Now, if both parallelograms are on the same base and also between the same parallels, then their heights will be equal.

Hence, their areas will also be equal.

∴ $\mathrm{ar}\left(\mathrm{ABCD}\right)=\mathrm{ar}\left(\mathrm{EFGH}\right)$