Let ABC be a triangle, and let its angle bisectors be AD, BE, and CF which intersect at I. If DI=3, BD=4 and BI=6 then compute the area of triangle BID.
We can use a really handy formula to help solve this question.
First, we have to calculate the semiperimeter of the triangle, which is half the sum of the three side.
We get 3+4+62=132
That may seem useless, but it will come in handy very soon.
Now, we apply Heron's Formula, which states that the area of a triangle is equal to √s(s−a)(s−b)(s−c). Subbing everything in, We get
Area=√132(132−3)(132−4)(132−6)
Area=√45516=√4554
So our final answer is √4554
Thanks! :)