# Problem of the Week Problem D That Triangle

In the diagram, $$ABCD$$ is a rectangle. Point $$E$$ is outside the rectangle so that $$\triangle AED$$ is an isosceles right-angled triangle with hypotenuse $$AD$$. Point $$F$$ is the midpoint of $$AD$$, and $$EF$$ is perpendicular to $$AD$$.

If $$BC=4$$ and $$AB=3$$, determine the area of $$\triangle EBD$$.