The task
How to play Area Balance
How much of this shape is one third? Slide a straight cut across an irregular polygon and try to leave the requested fraction on the shaded side. A cut one third of the way across is not necessarily one third of the area.
Make the shaded left or top portion equal the target fraction of the whole shape.
- Read the target percentage and check which side of the cut is shaded. A vertical line measures the left portion; a horizontal line measures the top portion.
- Move the cut until the shaded region looks like the requested share of the shape. Use the area of the shape itself, not the empty space around it.
- Submit to see the measured percentage, whether your portion was too large or too small, and the error in percentage points.
Phone, mouse and keyboard controls
Move the range control with a finger or mouse. The keyboard arrow keys make small adjustments while the range control is focused. The control changes the cut position; the result measures the polygon area on its shaded side.
Make your answer in the game, then use its Submit button when ready. Keep the game visible during the round. If an interruption requires another observation, the run is labeled Reviewed to distinguish it from an uninterrupted first attempt.
Know what your result means
How the score works
The game clips the polygon at your cut and divides the shaded area by the whole area. Let e be the absolute difference between your area fraction and the target fraction. Score = round(100 × exp(−0.5 × (e / 0.05)²)). Exact area scores 100; an error of 5 percentage points scores 61.
A worked example
For a 40% target, a shaded area of 45% has an error of 5 percentage points, so it scores 61. A 42% area is 2 points away and scores 92. These are area percentages, not the slider positions.
A score is feedback on this puzzle and these rules. Compare attempts with the same game, difficulty and puzzle conditions; a score from another type measures a different task.
Learn from the answer
Common mistakes and what to try next
Treating width as area
A wider part of the shape contributes more area for the same movement of the cut. Look at how much material the line sweeps through, not just how far it travels.
Measuring the wrong side
Check the shaded side before you answer. For a 25% target, leaving 75% shaded is the opposite answer even if the unshaded piece looks right.
Overcorrecting near the target
After a large adjustment, use smaller control movements. Review whether your answer was too large or too small before trying a related shape.
One change at a time
The targeted variation changes the shape’s proportions while preserving its target and cut direction. Use it to compare visual estimates across a narrower, taller version of the same polygon.
After a pack, the result suggests a focused variation for your lowest-scoring type. After that variation, retry it or choose a fresh practice pack. A replay is useful for learning, but its score should not be treated as a first unseen attempt.
Area Balance questions
Does putting the slider at 50% always split the area in half?
No. Slider position and area fraction are different measurements. The amount of shape on each side determines the result.
What does percentage-point error mean?
Subtract the target percentage from your measured percentage and take the absolute value. A 45% answer to a 40% target is 5 percentage points away.
Do I need a ruler or calculator?
No. The challenge is to estimate visually. The result calculates the actual polygon area so you can compare the estimate with a precise answer.