+1000 Let $ABCD$ and $BEDF$ be two $8 \times 9$ rectangles that overlap, as shown. Find the area of the overlap.
+1952 Ok, let's first let the intersection of AD and FB be Z.
We know AB = 8.
Lets let FZ = x
From the problem, we can tell that triangles ZFD and ZAB are congruent triangles. From this, we know FB = 9.
ZB = FB - FZ = 9 - x
Now, let's use the awesome pythaogrean theorem.
ZB2=FZ2+AB2(9−x)2=x2+82x2−18x+81=x2+6481−64=18x17=18xx=17/18
Now, we can find the non-shaded area.
4∗[ABZ]=4(1/2)(AB)(AZ)=4(1/2)(8)(17/18)=272/18=136/9
Now, the shaded area is 8∗9−136/9=72−136/9=512/9
Thanks! :)
