Area of Square $\neq$ the area of Rhombus created by stretched square? I have a problem where I am given a square with each side = to 3, that is stretched until points A and B are at a distance of 3 away from each other. Additionally, the length of the sides do not "stretch".
I thought that because area is base * height, that the area would not change due to this transformation.
In this case, the area of the square before transformation is 9, but the area of the rhombus is 7.794.
Why does the area change? 
Why is the area of the rhombus still not base times height?
Please note, I understand how to get the area of the rhombus - it just does not make sense intuitively and conflicts with the area of a parallelogram being b times h idea.

 A: The base length will not change, but the height will change. The height will no longer be a side length of the rhombus/parallelogram; it will be shorter.
A: It IS base times height but the  height has changed.  
The height is the perpendicular from line to line.  As a square the height was 3 as the sides were perpendicular.  You've squished the square over while keeping the sides the same but the sides are no longer perpendicular.  So the height is no longer the same thing as the sides.  The height is now less than 3.
A: The area of a rhombus and a square are not supposed to be same even with perfect stretching of square to form a rhombus.
A square is a SPECIAL RHOMBUS by all properties while a rhombus is not a SQUARE by some properties.
Two diagonals of square are the same while that rhombus are not.
Square has all its 90° while rhombus has only 2 pairs of opposite angles same.
Area of Square = s²  = p²/2    (if s is the side and p is diagonal)
Area of Rhombus = pq/2 (where p and q are diagonals of the rhombus. ≠ s²
To prove this, 
The diagonal of a rhombus p and q intersect at right angled  and form two equal isosceles triangles.
So area of rhombus is 
2 × Area of one of the triangles 
But 
Area of the triangle = 1/2 × base × height 
                               = 1/2 × s × p/2

                               = ps/4 ≠ s

