Area maze
Find the missing length using only whole-number areas.
The maths Area arithmetic without algebra
Find the length marked with a question mark. 3 rectangles, 4 facts given.
Every length here is a whole number. No fractions are needed.
Read the figure as text
A rectangle 9 wide and 5 tall, cut into 3 smaller rectangles. Rectangle A runs from 0 to 3 across and from 0 to 5 down. Rectangle B runs from 3 to 9 across and from 0 to 3 down. Rectangle C runs from 3 to 9 across and from 3 to 5 down. Given: the area of A is 15; the area of C is 12; the height of A is 5; the full width is 9. Find the height of B, marked with a question mark.
How to play
A big rectangle is cut into smaller ones. A number inside a rectangle, next to the small square mark, is that rectangle's area. A number sitting on an edge is a length. One length is replaced by a question mark, and that is the one to find.
Two facts do all the work. Area equals width times height, so knowing any two of the three gives you the third. And lengths lying end to end add up, so a long edge minus the pieces you know leaves the piece you do not. Work outwards from whatever you can already pin down. Every answer along the way is a whole number, so if a division does not come out exactly, that was not the right rectangle to start with.
Keyboard: Tab moves to the answer box, then to Check, then to the working button. Type the number and press Enter to check it. Show a step reveals one line of the reasoning at a time, in the order the deductions come.
Why this is mathematics
Every rectangle obeys area = width × height, and the rectangles share edges. Chain those facts and the missing number falls out — no equations, no fractions, just careful multiplication and division in the right order. Invented by Naoki Inaba for exactly this reason.