In ΔABC, MN || BC, the area of quadrilateral MBCN=130 sq cm. If AN : NC = 4 : 5, then the area of ΔMAN is:

32 cm²

Given,

The area of quadrilateral MBCN = 130 \( { cm}^{2 } \).

AN : NC = 4 : 5

Hence, AC = 4 + 5 = 9

In \(\Delta \)ABC, If MN is parallel BC, then

\(\frac{area\;of\;AMN}{area\;of\;ABC}\) = \( {(\frac{AN}{AC}) }^{2 } \)

\(\frac{area\;of\;AMN}{area\;of\;ABC}\) = \( {(\frac{4}{9} )}^{2 } \) = \(\frac{16}{81}\)

Area of \(\Delta \)AMN = 16 unit and area of \(\Delta \)ABC = 81 unit

Now, Area of quadrilateral MBCN = area of \(\Delta \)ABC - area of \(\Delta \)AMN

= (81 - 16) unit = 130 \( { cm}^{2 } \)

= 65 unit = 130 \( { cm}^{2 } \)

= 1 unit = 2 \( { cm}^{2 } \)

Therefore, area of \(\Delta \)AMN = 16 x 2 = 32 \( { cm}^{2 } \).