You can compute the visible height for a given distance from the camera using the formulas explained in Three.js – Width of view.
var vFOV = camera.fov * Math.PI / 180; // convert vertical fov to radians
var height = 2 * Math.tan( vFOV / 2 ) * dist; // visible height
In your case the camera FOV is 45 degrees, so
vFOV = PI/4.
(Note: in three.js the camera field-of-view FOV is the vertical one, not the horizontal one.)
The distance from the camera to the front face (important!) of the cube is 750 – 500 – 50 = 200. Therefore, the visible height in your case is
height = 2 * tan( PI/8 ) * 200 = 165.69.
Since the front face of the cube is 100 x 100, the fraction of the visible height represented by the cube is
fraction = 100 / 165.69 = 0.60.
So if you know the canvas height in pixels, then the height of the cube in pixels is 0.60 times that value.
The link I provided shows how to compute the visible width, so you can do that calculation in a similar fashion if you need it.