Geometry Area and Perimeter Builder
Use formulas for rectangles, triangles, circles and L-shapes while counting grid squares, and discover that shapes with the same perimeter can have very different areas.
Before you try
What if you had 24 metres of fence? Which shape gives your goat the most grass?
Try it out
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What happened?
Move a control to see what changes and why.
Shapes sit on a perfect grid with exact measurements. Real measuring always carries a little error.
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Try these ideas
- Make a rectangle with perimeter 20. Now find the one with the biggest area.
- Double the side of a square. Does the area double?
- Compare a circle and a square with the same perimeter.
Why it works
Perimeter is the distance around a shape; area is the space inside it. A rectangle’s area is length × width and its perimeter is 2 × (length + width). A triangle’s area is ½ × base × height. A circle’s circumference is 2πr and its area is πr².
Drag the sliders to resize each shape on a centimetre grid. The simulator counts the squares inside, shows the formula with your numbers, and lets you compare shapes with the same perimeter.
Check your understanding
Question 1 of 3
A rectangle is 6 cm long and 4 cm wide. What is its area?
What is the perimeter of the same 6 cm × 4 cm rectangle?
If you double every side of a square, the area becomes…
Explain it in your own words
What changed? Why did it happen? Where might you notice this in everyday life?
What will you discover next?
Try Pythagorean Theorem: Discover the Missing Side next.
For parents & teachers
- Measure a room and work out how much carpet (area) and skirting board (perimeter) it needs.
- Ask: why do farmers care about both fence length and field area?
- Find shapes at home with the same perimeter but different areas.