Area
Area is the amount of flat space a shape covers on a surface.
A baking tray has a flat surface. A large tray covers more table than a small one. That covered space is its area. Two trays side by side cover more flat space than one tray alone.
Explaining area by grade level
Think about a honeycomb. Each small cell covers a bit of flat space. That flat space is its area. Bigger cells cover more area, and smaller cells cover less.
Projects that explore area
A Koch snowflake grows by adding triangles to every side at each stage, which makes the edge longer but barely changes how much flat space the shape covers. After many stages, the snowflake's area ends up only 1.6 times the original triangle — finite, even as the edge grows without limit. You use power series to calculate this final area and prove that boundary length and covered surface can behave in completely different ways.
How much material a shape needs depends directly on the flat space it has to cover. In the Tiling Patterns project, you prove that hexagons use less wax than squares or triangles to create the same area. That result explains why bees choose hexagons — they get the most storage space from the least building material.