Area of a Rhombus: Finding Area based off Perimeter and Vice Versa

First, let's remember that according to the properties of a rhombus, all sides of a rhombus are equal,

Therefore, if we define the sides of the rhombus with the letters ABCD,

We can argue that:

AB=BC=CD=DA

We use the perimeter formula:

50 = AB+BC+CD+DA

And we can conclude that
 4AB=50

(We can also use any other side, it doesn't matter in this case because they are all equal.)

We divide by four and reveal that:

AB=BC=CD=DA = 12.5

Now let's remember the formula for the area of a rhombus: the height times the side corresponding to the height.

We are given the length of the external height 8,

Now, we can replace in the formula:

8*12.5=100