Question

If one of the side lengths of a parallelogram is increased and the other is held constant, what is the effect on its:
i. Perimeter?
_______________
ii. Area?
_______________

Answer 1

Step-by-step explanation:

A parallelogram and a rectangle have the same length of base and

Your calculation already answers your own question

Notice that when calculating the area of a rectangle, you did A=ab where as while calculating the area of a parallelogram, you did A=absinθ

Recall that

−1≤sinθ≤1

For the parallelogram, if we say b =base then, height =asinθ

So

−a≤asinθ≤a

It should be clear now, that when θ=90,asinθ=a

But this can happen only when the parallelogram turns into a rectangle. When you moved a pair of the parallel sides of the parallelogram to the left (or right), you changed the angle

Hence given the same dimensions, the area of a rectangle is more than that of a parallelogram.