That is TFT screen which divides the screen into small sections of using vertical lines. What i have found so far is that TFT LCDs are made using liquid crystals which are laid in such a way that they form each and every pixel of screen.
If you search for TFT on web you might get some construction information of the screen.
There are 2025 rectangles in a 9x9 grid.
That depends on how big the rectangles are.
4 rectangles
96 rectangles.
441
62 x 38 = 2356 rectangles
225
315
There are three varieties of pentagrids. Initial type - 6A7 type (converter). Grid 1 - oscillator grid, Grid 2 - oscillator anode, Grid 3 - screen grid, Grid 4 - signal grid, Grid 5 - screen grid. Development - 6SA7/1R5 type (converter). Grid 1 - oscillator grid, Grid 2 - screen grid, Grid 3 - signal grid, Grid 4 - screen grid, Grid 5 - suppressor grid. Development - 6L7 (mixer). Grid 1 - signal grid, Grid 2 - screen grid, Grid 3 - oscillator injection grid, Grid 4 - screen grid, Grid 5 - suppressor grid.
36
90
14