need help with right triangle

Using the Pythagorean Theorem, CD = 2.4. We notice that $\bigtriangleup$ABC is similar to $\bigtriangleup$ACD (this is a 3-4-5 right triangle). Since AC is the shorter side, it is 3, BC is 4, and AB is 5, so the area of a 3-4-5 triangle is 3x4/2 which is 6.

We can check if BD is 3.2.

$2.4/x = 3/4$ so BD = 3.2. 

So all of our work adds up; the area of $\bigtriangleup$ABC is 6.