Step 1: Recall the relation between the areas of the similar triangles.

            THEOREM: The ratio of the areas of two similar triangles is equal to the

            ratio of the squares of their corresponding sides

             \frac{Area \triangle ABC}{Area \triangle DEF} = (\frac{AB}{DE})^2 = (\frac{BC}{EF})^2 = (\frac{CA}{FD})^2   

Step 2: Substitute all the known values in the theorem

            EXAMPLE:   \frac{Area \triangle ABC}{Area \triangle DEF} =(\frac{BC}{EF})^2

                          = \frac{54}{Area\ of\ \triangle DEF}=(\frac{3}{4})^2

Step 3: Simplify for the unknown value

          EXAMPLE:  Area\ of\ the\ \triangle DEF\ =\frac{16}{9}*\ 54

                              Area of the \triangle DEF = 16 * 6

                                Area of the \triangle DEF = 96 cm^2