State true or false:

All parallelograms having equal bases have the same areas.

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True

False

answer is B.

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Detailed Solution

Here, we have to find whether the parallelograms that have equal bases have the same areas or not.
The area of a parallelogram is obtained by the product of its base length and its height.
If a number of parallelograms have the same base lengths, but different altitudes, then their area can never be equal. It can be equal only and only if they have the same base lengths and the same altitudes.
So, we conclude that having the same base lengths does not guarantee that the area of the parallelograms will be equal.
It requires that their altitudes must also be equal.
Hence, the statement is false.
So, all parallelograms having equal bases have the same areas only when their altitudes are also the same.
Hence, the correct option is (2).

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