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 = 8, then find the area of triangle ABC.
+8 The area of a triangle is given by:
Area = 1/2 x base x height
We have,
A triangle ABC.
Angle bisectors are AD, BE, and CF, which intersect at I.
DI = 3
DI = AI = 3
Height of the triangle = AD = AI + DI = 3 + 3 = 6
BD = 4 = BC
Base of the triangle = BC = BD + DC = 4 + 4 = 8
The area of a triangle:
= 1/2 x base x height
= 1/2 x 8 x 6
= 1 x 4 x 6
= 24
Thus,
The area of the triangle is 24.
