Call the missing area x^2.

Let the base of the rectangle equal 2x/c (where x is positive, c is just an arbitrary scaling factor).

Since the area of a triangle is half base times height, the height of the missing triangle is xc.

Since the 4-triangle is similar to the missing triangle, the height of that is 2c (as 2^2=4), so the overall height of the rectangle is (xc+2c).

The area of the overall rectangle can now be written is two distinct ways, which must be equal:

Summing the four regions: x^2+15+4+26

Rectangle base times height: 2x^2+4x (notice the c vanishes)

Equating those two expressions and bringing everything to one side gives:

x^2+4x-45=0

which we can factorise into:

(x+9)(x-5)=0

The positive root is x=5, so the missing area x^2 is 25.