Question

Two parallelograms have pairs of sides that are 3 feet long and 2 feet long. One of the parallelograms is a rectangel and the otehr is not. Which has a bigger area, and why?

Answer 1

If they both have the same hight and the same length then they both have the same area. So if what you are saying is that both shapes have two sides that are 3 feet long and the other pair of lines are 2 feet long then both shapes have the same area.

Answer 2

The rectangle.

You can see this visually if you draw a rectangle that is 2" high and 3" wide, and then compare that to a parallelogram drawn with the same dimensions but that is very highly "tilted", such that the distance between the top and bottom sides is close to 0.

If you prefer a more mathematically reasoned explanation. Draw a parallelogram with sides 2" and 3" long, with interior angles that are 45 and 125 degrees. Now drop a vertical line down from the upper 135 degree angle down to the horizontal side. That is the height of the parallelogram.

The area of a parallelogram is base times height: a = b(h)

The length of the base is 3" no matter what angle we use, so it drops out, leaving us with:

a ~ h

where ~ means proportional to.

So if we can increase the height of the parallelogram, we will increase the area. Can we do that? Yes.

Imagine the parallelogram is a cardboard box, so that we can adjust the angle. Slowly push on the sides so that the parallelogram gets, overall, narrower and ... yes ... taller. Each incremental change increases the area of the parallelogram, since the height increases.

In fact, you will have maximized the area of the parallelogram when you reach a rectangle.

Answer 3

i say that they both are larallelo