Step 1: Know about the isosceles right triangle

        NOTE: Triangle is isosceles right triangle, the length of two sides will be

              equal. And Pythagoras Law is applicable.

Step 2: Assume any variables as lengths of the isosceles right triangle.

             NOTE: Let "x" be the length of one equal side, and "y" be the length of

                       hypotenuse side

Step 3: Set up an equation using the variables and given perimeter measurement.

             EXAMPLE: perimeter of triangle = 6 + 3 \sqrt{2}

                                       x + x + y = 6 + 3 \sqrt{2}   

                                       2x + y = 6 + 3 \sqrt{2} -----------------(1)

Step 4: Find the "y" value by using the Pythagoras Law.

            EXAMPLE: y^2 = x^2 + x^2

                               y^2 = 2x^2

                               y = \sqrt{2}x

Step 5: Substitute y value in the equation (1) (see step 3). To find the length.

            EXAMPLE:  2x + y = 6 + 3 \sqrt{2}

                         2x + \sqrt{2}x = 6 + 3 \sqrt{2}

                                            x = 3

Step 6: Plug the base and height into your area formula.

              x length of the equal side = 3

             \frac{1}{2}b*h  =   \frac{1}{2} (3*3)

                                                          = 4.5 square meter