In $$\triangle$$ ABC, MN $$\parallel$$ BC, the area of quadrilateral MBCN=130 sqcm. If AN : NC = 4 : 5, then the area of $$\triangle$$ MAN is:

AN : NC = 4 : 5

AC = AN + NC = 4 + 5 = 9

MN $$\parallel$$ BC

So,

$$\triangle$$ ABC ~ $$\triangle$$ MAN

$$\frac{Area of \triangle MAN}{Area of \triangle ABC} = \frac{4^2}{9^2}$$

$$\frac{Area of \triangle MAN}{Area of \triangle ABC} = \frac{16}{81}$$

Let the area of $$\triangle MAN$$ be 16x and $$\triangle ABC$$ be 81x.

Area of  quadrilateral MBCN =130 sqcm

Area of $$\triangle ABC$$ - area of $$\triangle MAN$$ =130 sqcm

81x - 16x = 130

x = 130/65 = 2

Area of $$\triangle$$ MAN = 16x = 16 $$\times$$ 2 = 32 sqcm.