Answer:
[tex]\huge\boxed{A=24\sqrt2}[/tex]
Step-by-step explanation:
Look at the pictures.
In the ΔAED the sides are in the proportion [tex]1:1:\sqrt2[/tex]
Therefore we have the equation:
[tex]|AE|\sqrt2=6\qquad\text{multiply both sides by}\ \sqrt2\\\\2|AE|=6\sqrt2\qquad\text{divide both sides by 2}\\\\|AE|=3\sqrt2[/tex]
Therefore
[tex]|ED|=3\sqrt2[/tex]
The formula of an area of a parallelogram:
[tex]A=bh\\\\b-base\\h-height[/tex]
We have
[tex]base=|AB|=8\\height=|ED|=3\sqrt2[/tex]
Substitute:
[tex]A=(8)(3\sqrt2)=24\sqrt2[/tex]
