Awall in maria’s bedroom is in the shape of a trapezoid. the wall can be divided into a rectangle and a triangle.  using the 45°-45°-90° triangle theorem, find the value of h, the height of the wall.

You don't provide much info here.  A drawing of the wall would be useful.  You'll need to choose variables (x, y, h, and so on) to represent the dimensions of the trapezoid and its parts (the rectangular bottom part and the triangular top part).  The area of the trapezoidal shape is the sum of the areas of the rectangle and the triangle.

Suppose that the horiz. measurement of the rectangle is x and that the vertical meas. is y.  Then the area of the rectangle is Ar = xy.

Suppose that the horiz. base of the triangle is x (same as the horiz. measurement of the rectangle.  Let the vert. height of the triangle be y.
Then the area of the triangle is At = (xy)/2 (standard formula for the area of a triangle)

Then the area of the trapezoid is the sum of the areas of the rectangle and triangle:

A = xy + (xh)/2

Without more info (e. g., the values of x, y and h), we can proceed no further.