Geometry

D is on side AC of Triangle ABC. We know [ABC] = 120, AD = 8, DC = 3. What is [ABD]?

~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

Let ΔABC be the right triangle.

If AD = 8, DC = 3, and [ABC] = 120, then AB = 21 ⁹/₁₁

[ABD] = 1/2(AD * AB) = 87 ³/₁₁ square units

Triangles   ABD    and   CBD  will  be  under  the  same  height

So     [ABD]  =    (8 / ( 3 + 8) )  *  120   =   (8)(120)  /11  = 960/11    ≈  87.27