Area of triangle ABD?

A normal-level "Area" problem."Shared apex, bases on one line" means the area ratio equals the base ratio. The most-used tool in geometry problems.

GivenTriangle ABC has area 60 cm². BD : DC = 3 : 2

Hints

Triangle ABD and triangle ABC both have A as their apex, so they share the same height.
With the same height, area is proportional to the base. BD : DC = 3 : 2, so the blue and orange areas are in the ratio 3 : 2 too.
So let's cut base BC into 5 equal parts and draw lines from A.
Every slice has the same base and the same height, so all 5 pieces are equal in area. Triangle ABC is 5 of these equal pieces.
Of those, the red triangle ABD is 3 pieces — that is 3/5 of the whole.
The whole is 60 cm², so 60 ÷ 5 × 3 gives the answer.

Answer 36cm²