Geoboard

← Teacher Binder

Click pegs to build a polygon, one vertex at a time. Click the first peg again (or hit Close shape) to close the polygon and see its perimeter and area. Perimeter is in peg units; area uses the shoelace formula and is reported in square peg units.

Perimeter
0
units
Area
0
square units

How it works

Perimeter: sum of side lengths. Diagonal sides are non-integer (Pythagoras).

Area: uses the shoelace formula, which gives the correct area for any simple polygon (no crossing sides).

Pick's theorem (Grade 7+): for a polygon with vertices on grid points, Area = I + B/2 - 1, where I is interior lattice points and B is boundary lattice points. Try checking against the shoelace value.

Try these

3x3 square Perimeter 12, area 9.

Right triangle 3-4-5 Perimeter 12, area 6.

Pentagon 5 vertices, no two on the same row or column.

Concave shape A six-sided polygon with one inward bend (must not cross itself).