Learning goals
- Area counts the tiles inside the shape.
- Perimeter walks the outside boundary.
- Two rectangles can have the same area but different perimeters.
Grid Tiling & Boundary
Area versus perimeter
Change a rectangle freely and watch area and perimeter update separately.
What this game shows · Area vs. Perimeter
Area measures the inside; perimeter measures the boundary. Two rectangles can share an area but disagree on perimeter (and vice versa). This sandbox lets you change rows and columns and watch both numbers update separately so the difference becomes obvious.
- Area
- rows × columns — how many unit tiles fit inside.
- Perimeter
- 2 × (rows + columns) — distance around the outside.
- Same area ≠ same perimeter
- 4 × 3 and 6 × 2 both = 12 area, but perimeters are 14 and 16.
Aligned with CCSS 3.MD.D.8 (perimeter and area of polygons).
Tiling and boundary
Area counts inside tiles. Perimeter walks the outside edge.
A 12 / P 14
Height
3
Width
4
Geometry and measurement model
Who this demo helps, and where to practice next
Grid Tiling & Boundary is built for students who memorize formulas before seeing the shape decomposition. It gives the page a clear search purpose: learn the model, manipulate it, then continue into the matching grade-level practice.
Grid Tiling & Boundary helps when a student can copy a procedure but cannot explain why it works. The demo slows the idea down into a visible model before sending the learner to guided missions.
How to play
- 1 Identify the shape pieces before calculating.
- 2 Drag or replay the model until the formula can be described from the picture.
- 3 Open the related geometry topic when the student can explain area, perimeter, or surface area in units.
Continue with guided practice
FAQ
Tap to expand Area and perimeter, separated.
01 Why are area and perimeter different things? 2-D vs 1-D
Area is a 2-D measure (square units). Perimeter is a 1-D measure (units). They scale at different rates, so they answer different questions.
02 How can two shapes have the same area but different perimeter? 12 area, 14 vs 16
4×3 and 6×2 both contain 12 tiles. But their perimeters are 14 and 16 — the long-skinny shape walks farther around its boundary.
03 When do you want maximum area for a given perimeter? Square is best
A square wins. Among all rectangles with a fixed perimeter, the square has the largest area. The game makes this visible by squeezing the rectangle.
04 Which grade is this game for? Grades 3–4
Grades 3–4, aligned with CCSS 3.MD.D.8. Direct ramp to optimization questions in Grade 6.