Question

a quadrilateral has four sides of length 7, what are the possible areas of the polygon?

Answer 1

7 x 7 = 49

Answer 2

I don't know how to answer this without just giving out the answer, but...

Arranging the sides as a 7*7 square yields the maximum area attainable.

However, if you push the top edge over so that the square becomes a parallelogram, the height decreases while the base remains constant. This reduces the area enclosed by the 4 sides.

You can also continue pushing until the parallelogram's height becomes zero. At that moment, it is no longer a quadrilateral.

So the "possible areas" definable by these 4 sides is >0 to 49.

Answer 3

@Calhelp

When you study Calculus, you can prove what @qweqwe123123123123111 said:
For a fixed perimeter of a rectangle, a square maximizes area for that given perimeter.