In triangle $ABC,$ angle bisectors $\overline{AD},$ $\overline{BE},$ and $\overline{CF}$ meet at $I.$ If $DI = 3,$ $BD = 4,$ and $BI = 5,$ then find the area of triangle $ABC.$

Select all the correct locations on the table. consider the following expression. 76.493 select "equivalent" or "not equivalent" to indicate whether the expression above is equivalent or not equivalent to the values or expressions in the last column equivalent not equivalent 343 equivalent not equivalent 49 78.498 78.498 75.493 equivalent not equivalent 75.7 equivalent not equivalent