83 Area of parallelogram

[ern5231]

A parallelogram has one side length=6 and another side length=7. What could be the possible area?
I 21
II 42
III 81

The OA speaks of having 21 as the valid answer. How is that possible?

[ashis979]

21 it is.

I: Parallelogram with base 7
Since the base is 7, the other side is 6. 6 also the hypotensue of the right triangle that you will draw in order to determine the height of the parallelogram. However, no calcs necessary. Since 6 is the hypotenuse, the height has to be less than 6 and the area of the parallelogram would be 7*less than 6 = less than 42...go with I

II. Parallelogram with base 6
Same as above. In this case the hypotenuse is 7 and therefore the base must be less than 7. So area of the parallelogram would be 6*less than 7 = less than 42...again, go with I

[sanjana]

I agree with 21,But couldnt the answer also be 42
If we make the 2 sides perpendicular to eachother,it becomes a rectangle which is also a parallelogram and the area will be 6*7.

Are we not considering this case because the question mentions Parallelogram?
I'm confused! :roll:

[ashis979]

I avoided considering a rectangle assuming that the question would have made that distinction. Not to mention 42 seemed like too obvious a choice. But you are correct to assess that it could very well be just 6*7=42 or the other way around. I have certainly seen questions like "Is ABCD a parallelogram?" where you need to consider all possibilities, rect, sq, rhom.