The Area Builder simulation from PhET lets you build your own shapes with colorful blocks and explore how area and perimeter are related. You can compare two shapes side by side, and challenge yourself in the game to build shapes or find the area of funky figures. It is free, runs in any browser on a phone, tablet or laptop, and it is a great fit for the area, perimeter and mensuration lessons in Tamil Nadu State Board (Samacheer Kalvi) Maths.
What is the Area Builder simulation?
This interactive simulation lets you build shapes from unit blocks and see their area and perimeter. You can build shapes with a given area or perimeter, compare two shapes, and find the area of irregular shapes by splitting them into simpler ones. Because it runs on HTML5, there is nothing to install, and it works on phones, tablets, Chromebooks and computers.
Elementary and middle school
Area, perimeter and scale factor
Phone, tablet, Chromebook, PC
English
PhET’s learning goals are to find a shape’s area by counting unit squares, to describe the relationship between area and perimeter, to build shapes with a given area, perimeter or both, to find the area of an irregular shape by splitting it, and to see how area and perimeter change when a shape is scaled.
Launch the Area Builder simulation online
Tap or click inside the player and start exploring. Use the full-screen button in the player for a bigger view.
Credit: University of Colorado Boulder
How to use the Area Builder simulation, step by step
- Predict first. Before you build, guess the area and the perimeter of the shape you plan to make.
- Build a shape. Place blocks to make a shape and count the unit squares to find its area.
- Find the perimeter. Count the units around the outside edge of the shape.
- Compare two shapes. Build two shapes with the same area but different perimeters, or the other way round.
- Take the game challenge. Build shapes to match a goal, or find the area of an irregular figure by splitting it into smaller shapes.
Tip for students: count the unit squares first, then check your answer with the formula.
The idea behind the simulation: area and perimeter
A = l × w, P = 2(l + w)
For a rectangle with length l and width w, the area A is the number of unit squares inside it, and the perimeter P is the distance around it. If you scale a shape by a factor k, every length is multiplied by k, so the perimeter is multiplied by k and the area is multiplied by k × k.
Worked example: A rectangle is 4 units long and 3 units wide. Its area is 4 × 3 = 12 square units and its perimeter is 2 × (4 + 3) = 14 units. Scale it by 2 to get 8 by 6. The perimeter becomes 28 (twice as much) and the area becomes 48 (four times as much).
Area and perimeter key terms explained
These are the words you will meet while using the Area Builder simulation, with simple meanings.
Area
The amount of flat space inside a shape, counted in square units.
Perimeter
The distance around the outside of a shape.
Unit square
A square with sides of 1 unit. It has an area of 1 square unit.
Irregular shape
A shape that is not a simple rectangle, such as an L-shape.
Decomposition
Splitting a shape into smaller, simpler shapes to find its area.
Scale factor
The number you multiply every length by to make a bigger or smaller similar shape.
Similar shapes
Shapes with the same form but a different size.
Square units
The unit of area, such as square centimetres (cm²).
Common mistakes: Mixing up area and perimeter, forgetting to write square units for area, and thinking that doubling the sides also doubles the area when it actually makes it four times bigger.
Try the area and perimeter calculator (practice what you explore)
Enter the length and the width of a rectangle and a scale factor to see the area and the perimeter before and after scaling. Then tap a “what if” button.
What happens when you change a variable
| Change | Effect |
|---|---|
| Add a block to a shape | The area goes up by 1 square unit |
| Scale all lengths by 2 | Perimeter × 2, area × 4 |
| Scale all lengths by 3 | Perimeter × 3, area × 9 |
| Make a long thin rectangle with the same area | The perimeter gets bigger |
| Make the shape closer to a square (same area) | The perimeter gets smaller |
Classroom activities for teachers
The Area Builder simulation fits a single 40-minute period.
- Count first (10 min): students build shapes and count the unit squares before using any formula.
- Same area, different perimeter (10 min): students build two shapes with the same area and compare their perimeters.
- Split the shape (10 min): students find the area of an irregular shape by splitting it into rectangles.
- Exit ticket (10 min): students explain in two sentences why doubling the sides makes the area four times bigger.
Looking for the matching chapters? Browse the Maths books on TN SchoolBooks and download the Samacheer Kalvi PDFs, then use this simulation to make the area and perimeter lessons visual. More free simulations and textbook PDFs are on the home page.
Quick quiz: test your understanding of area and perimeter
Score: 0 / 5
Area Builder simulation: frequently asked questions
Is the Area Builder simulation free?
Yes. PhET simulations are free to run online in a browser. Check PhET’s licensing page for reuse terms.
Does it work on a mobile phone?
Yes. It is built with HTML5 and works on phones, tablets and Chromebooks. Use landscape mode or the player’s full-screen button for a bigger view.
What is the difference between area and perimeter?
Area is the space inside a shape, measured in square units. Perimeter is the distance around the outside of the shape, measured in units of length.
Can two shapes have the same area but different perimeters?
Yes. A 4 by 3 rectangle and a 6 by 2 rectangle both have an area of 12, but their perimeters are 14 and 16. Building such pairs is a great way to use the simulation.
The Area Builder simulation turns area and perimeter into something you can build, count and see. Explore it, take the quiz above, and keep building until finding the area of any shape feels easy.