Find the missing sides for angle abc below. and the solve for the area of angle abc

There is a 45,45,90 triangle and a 30,60,90 triangle within triangle ABC.

So you can just use the relationships between sides in these special triangles to find the desired lengths.

AB=3√2

z=3

b=3 (It is isosceles so we know that b=z)

With b=3, we know that...

x=3·2=6

y=3√3

answers: z=3,b=3,x=6,y=3√3