Draw a diagonal across from the top left corner of Y to its bottom right corner. We get a parallelogram with interior angles of 135° and 45°. Do the same for X to get a longer parallelogram with the interior angles of the same values.
Since parallelograms's opposite sides are of equal lengths, then the diagonal of square X and Y also equals 11.75cm. These two squares are congruent/identical.
Half of this diagonal equals the height of each of the two triangles in the square.
Area of 2 squares = area of 4 triangles
= 4 x ½ x b x h
= 2 x b x h
= 2 x 11.75 x 11.75/2
= 11.75 x 11.75
= 138.0625
= 138.06 cm² (to 2 decimal places)
Alternatively, area of 2 squares
= 2 x ½ x diagonal x diagonal
= diagonal x diagonal
= 11.75 x 11.75 (gives same answer as above)