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Mathematics
Area builder: area and perimeter
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Build shapes from unit squares on a grid. Area is the number of unit squares that cover the shape; perimeter is the number of unit edges around it, including around holes. The Game mode has six levels of building shapes and finding areas.
Drag from the box or tap the grid to build. New squares must share an edge; tap a filled square to remove it.
Keyboard: Tab to the board, arrows move the cursor, Enter or Space adds/removes a square, Delete removes.
Colour and display
Square colour
New squares take the chosen colour; colour does not change area or perimeter.
Show
Area: 12 square units Perimeter: 14 units
Area = number of unit squares covering the shape.
Perimeter = number of unit edges around the shape, including around holes.
Pink edges are the edges counted in the perimeter; each piece between two dots is one unit.
Numbers in the squares count the squares (the last one is the area); pink numbers along the edges count the unit edges (the last one is the perimeter).
Model notes
- A square on screen is an agreed unit square, not 1 cm. Area is measured in "square units" and perimeter in "units" (the length of one side of a unit square).
- Area is the number of unit squares that cover the shape. The game also has half squares (triangles): two halves make one unit square.
- Perimeter is the number of unit edges between the shape and everything that is not the shape, including the edges around holes. So cutting a hole lowers the area but raises the perimeter.
- Each board keeps one edge-connected shape: a new square must share an edge with the shape; touching only at a corner does not connect. When removing a square splits the shape, the part with more squares stays and the rest goes back to the box.
- A hole is a group of empty squares closed in by the shape. An empty square that meets the outside only at a corner is still a hole; a notch open to the outside is not.
- Side lengths are written only on straight runs of whole units; overlapping labels are hidden for now, zoom in to see them all. Slanted edges of half squares have no length label.
- Game challenges are generated at random, checked, and always solvable on the 12 × 8 board; the sample solution is only one of many. Colour fractions are compared in lowest terms (6/16 = 3/8).
- Points and the timer are for self-practice. Reloading the page returns an unfinished level to the level screen; the best score and best time of each level are kept.