I can get everything but the area can you help me?
Hello, jwein4492!
In the following diagram, NDBA is a rectangle,
$\displaystyle AN = NG,\;BF = DB,\;GD = 11,\;DF = 8\sqrt{2}$
What is the area of parallelogram $\displaystyle GDFA$ ?
Code:A G 11 D * - - - - - * - - - - - - * | * * | | * _ * | | * 8√2 * | x | * * | | * * | * - - - - - - * - - - - - * A F x B
We know the base of the parallelogram: .$\displaystyle GD = 11$
We need the height, $\displaystyle DB = x.$
Since $\displaystyle BF = DB,\;\Delta DBF$ is a 45° right triangle.
Using Pythagorus: .$\displaystyle x^2 + x^2 \:=\:\left(8\sqrt{2}\right)^2\quad\Rightarrow\quad 2x^2 \:=\:128\quad\Rightarrow\quad x^2 \:=\:64$
Therefore: .$\displaystyle x \:=\:8$
Got it?