How can I solve this menseki (area maze) puzzle?

[John Salerno]

Hi everyone. I just got a game for the Nintendo Switch called Menseki Genius, which has Area Maze puzzles in it. I've been staring at the very first puzzle for quite a while, and I'm stumped. Attached is an image of it.

My initial figuring was that since the rectangles with areas 11 and 13 are prime numbers, their lengths and widths have to be 11x1 and 13x1, respectively. Working from there, I figured out some other sides, like the other side of the 22cm rectangle being 2, etc.

But this isn't making complete sense, because that would make one of the sides of the 20cm rectangle 12, which has to be wrong.

I've tried looking up how to solve these puzzles, but every example I've seen so far shows the puzzle with some of the full side lengths being revealed as well, but this puzzle in question doesn't show those. It only shows the areas of the rectangles.

What am I doing wrong? How should I be approaching this?

(FYI: no fractions or decimals are used, and the proportions are not necessarily visually accurate)

Here is the image. The numbers in blue notes are my own guesses and are not a part of the original puzzle.

Edited May 31, 2022 by John Salerno

[Endy0816]

Yeah not sure dimensions actually make sense, but area should be:

((12 × 22 )/11) + ((20×13)/10)

You want to multiply two areas together then divide by the area of the rectangle they both share one side with, to find the area of one portion of the unknown area.

(AB × CD)/(BC) = AD

One possibility is that the unknown area isn't actually a rectangle(though is depicted as such).

Edited June 1, 2022 by Endy0816