Fence Area
A hands-on area and perimeter puzzle on a farm. Paint a sheep pen that covers exactly the target area and needs exactly the target length of fence, with every sheep inside and the trees outside. Learn why the same area can need very different fences.
Play nowHow to play
Controls
Drag- Drag across the grid to paint squares into the pen; start a drag on a pen square to erase instead. The two cards at the top show the pen's area (how many squares) and its fence (how many square edges run along the outside), next to the goals.
- A fence is drawn around your pen as you paint. The pen must be a single piece, must not have empty gaps inside it, must contain every sheep and must not include any tree.
- When area and fence both match and the rules are met, the farm is solved. A compact, square-like pen needs the least fence; long, thin or bumpy shapes need more, so stretch or dent your shape to change the fence without changing the area.
- HINT briefly shows one correct pen. Solve without hints and without too many edits for three stars.
About the game
Fence Area turns a classic school idea into something you can play with: area and perimeter are not the same thing. Every farm asks for a sheep pen of a certain size, counted in squares, and a certain length of fence, counted in square edges. You paint the pen yourself, and as you add or remove squares, a wooden fence follows the outline and two counters show the area and the fence length change.
Pretty quickly the main lesson becomes a feeling. A pen of twelve squares can be a tidy rectangle that needs fourteen fence lengths, or a long strip or a bumpy shape that needs eighteen or more. Adding a square in a corner can leave the fence unchanged, while adding one on a straight side makes it grow by two. Each farm also places sheep that must be inside and trees that must stay out, so you cannot just reuse the same shape everywhere, and the pen must be a single piece with no empty holes. Every farm was generated from a real pen, so there is always an answer, and a hint can flash one. Eighteen farms grow from a small 5 by 5 field to 8 by 9 pastures.
Free to play in your browser. No download, no sign-up. Works on phones, tablets and computers. Your progress is saved on this device.