In acute triangle $ABC,$ $\angle A = 45^\circ.$  Let $D$ be the foot of the altitude from $A$ to $\overline{BC}.$  if $BD = 2$ and $CD = 3,$ then find the area of triangle $ABC.$
<|im_start|>system
You are a helpful assistant.<|im_end|>
<|im_start|>user
In acute triangle $ABC,$ $\angle A = 45^\circ.$  Let $D$ be the foot of the altitude from $A$ to $\overline{BC}.$  if $BD = 2$ and $CD = 3,$ then find the area of triangle $ABC.$
Please reason step by step, and put your final answer within \boxed{{}}.<|im_end|>
<|im_start|>assistant

user
15
In acute triangle $ABC,$ $\angle A = 45^\circ.$  Let $D$ be the foot of the altitude from $A$ to $\overline{BC}.$  if $BD = 2$ and $CD = 3,$ then find the area of triangle $ABC.$
train