Bring kids outside to construct oversized polygons out of crepe paper or tape! Encourage kids to work together to create regular polygons (sides same length and angles equal) and irregular polygons. Split kids up into teams and have each team in charge of a polygon. Older kids can use a tape measurer to construct their shapes' sides. For younger kids, have them use the length of their body (non standard measuring) to construct sides. As you create the sides of your shapes, tape the crepe paper down on the pavement. Once all your sides are measured, find the perimeter. Then, have the kids walk around and identify their friends' shapes. Have them differentiate between a regular and irregular polygon. Point out quadrilaterals and quadrangles among peers' creations.
I recommend using colored masking tape. Tape stretches to create a nice, straight line. Crepe paper works well too, but avoid windy days!