Aera mazes use only the rectangle area formula to solve. You are to find the missing value, which is denoted by a question mark highlighted in grey. The only mathematics you need to know is that the area of a rectangle is the length multiplied by the width, and you are NOT allowed to use fractions in the solutions, needless to say, algebra.
Solution to the above: adding the two pink rectangles allows us to find
? = (38+39+21) / 7 * 6 - 24 - 40 = 20
The solution is to copy the 21 rectangle and paste it on the 43, we will get the blue rectangle below to have an area of 29. Since 4x10=40, so the green one at bottom right corner has an area of 11. The one on top is 22 because 43-21=22. Since the top one is twice as big as the bottom, the height on top must be 2x4=8. That gives us 8x10=80, so grey= 80-43=37.
As we can tell, the key is to cut and paste to make the rectangles aligned perfectly so you can use see the relationships among the unknowns. Now your homework is:
If you need a bigger challenge, try this:
A simple rough solution:
1. starting from upper left corner, it's not hard to find one side of the grey rectangle is 5. (Please note that the middle step 21/4 is not necessary as we can derive side length 8 by doubling the side length 4 of the 21 cm^2 rectangle. )
2. from the blue 5, we can derive the pink 5, which leads to the vertical side = 8 in the rectangle next to the grey one. From there, since we know the solution has to be a whole number, it's intuitive to guess the solution has to be 7. A quick verification: 7*5=35, 35+55+16=106, given the small piece not included yet, we look for the next multiple of 7 which is 112. That gives the small piece = 112-106 = 6. 112/7 = 16. 16=5+2+8+1, so everything seems fine.
A detailed solution of the above has many more steps, it can be found at the bottom of this page.