The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively.

Given: The corresponding altitudes of two similar triangles are 6 cm and 9 cm respectively.

To find: Ratio of areas of triangle.

We know that the ratio of areas of two similar triangles is equal to the ratio of squares of their corresponding altitudes.

$\frac{\operatorname{ar}(\text { triangle } 1)}{\operatorname{ar}(\text { triangle } 2)}=\left(\frac{\text { altitude1 }}{\text { altitude } 2}\right)^{2}$

$\frac{\operatorname{ar}(\text { trianglel })}{\operatorname{ar}(\text { triangle } 2)}=\left(\frac{6}{9}\right)^{2}$

$\frac{a r(\text { trianglel })}{a r(\text { triangle } 2)}=\frac{4}{9}$