if a square and a rhombus stand on same base , prove area of square has larger area

Consider the figure,

Here, square ABCD and rhombus ABEF lie on the same base AB. So,
Let the height of the rhombus be h.

Now, we know that
Area of square ABCD = b * b  ...(1)
Area of rhombus ABEF = b * h  ...(2)

Next, from the above figure it can be observed that the maximum value which h can take is equal to b.
Thus, h < b.
So, from (1) and (2)
b*b > b*h

Therefore, the area of square will be greater than the area of rhombus.