geometry - Tiling rectangles with T pentomino plus rectangles

Inspired by Polyomino Z pentomino and rectangle packing into rectangle

Also in this series: Tiling rectangles with F pentomino plus rectangles

Tiling rectangles with N pentomino plus rectangles

Tiling rectangles with U pentomino plus rectangles

Tiling rectangles with V pentomino plus rectangles

Tiling rectangles with W pentomino plus rectangles

Tiling rectangles with X pentomino plus rectangles

The goal is to tile rectangles as small as possible with the T pentomino. Of course this is impossible, so we allow the addition of copies of a rectangle. For each rectangle $a\times b$, find the smallest area larger rectangle that copies of $a\times b$ plus at least one T-pentomino will tile. Examples shown, with the $1\times 1$ or the $1\times 2$, you can tile a $3\times 3$ as follows:

Now we don't need to consider $1\times 1$ or $1\times 2$ any longer as we have found the smallest rectangle tilable with copies of T plus copies of $1\times 1$ and $1\times 2$.

There are at least 10 more solutions. I tagged it 'computer-puzzle' but you can certainly work some of these out by hand. The larger ones might be a bit challenging.

Answer

I assume these are the remaining ones you found as well; for 2x3

a simple 7x5 = 35 one:

for 2x2

a 10x8 = 80 one

for 1x5:

11x10 = 110

for 2x4:

14x22 = 308

for 2x5:

12x15 = 180

for 3x4:

18x19 = 342

and finally a large one for 3x5

which uses the same central figure formed by the Ts as the 1x5.
28x40 = 1120