Finding the area of a triangle

Question

I apologize for my bad English in advance. The area of triangle ABC is equal to 1 m². Point D is on edge AB and 2 AD = DB. Point E is on edge BC and 3 BE = 2 EC. What is the area of triangle DBE?

Answer 1

Use sine formula $$S=\frac{1}{2}AB\times BC\times \sin B=1$$ $$S'=\frac{1}{2}BD\times BE\times \sin B=\frac{1}{2}\frac{2}{3}AB\frac{2}{5}BC \sin B=\frac{4}{15}S=\frac{4}{15}$$