Plane Geometry Explorer
Visualize and calculate properties of geometric shapes
Learning Tip: Adjust the properties and click "Calculate" to see immediate results.
Shapes
Shape Properties
Select a shape to view and edit its properties
Select a shape to begin visualization
Calculated Properties
Properties will appear after calculation
Formulas
Formulas will appear here
Essential Plane Geometry Concepts
Shape Properties
- Perimeter: Sum of all side lengths
- Area: Space enclosed by the shape
- Angles: Important for polygon classification
- Symmetry: Lines of reflectional symmetry
Key Formulas
- Triangle Area: ½ × base × height
- Circle Area: π × radius²
- Rectangle Area: length × width
- Polygon Angles: (n-2) × 180°
Shape Classification Guide
| Shape | Sides | Angles | Symmetry | Special Cases |
|---|---|---|---|---|
| Triangle | 3 | Sum to 180° | 0-3 lines | Equilateral, Isosceles, Scalene |
| Quadrilateral | 4 | Sum to 360° | 0-4 lines | Square, Rectangle, Rhombus, etc. |
| Circle | 1 (curve) | N/A | Infinite | N/A |
| Regular Polygon | n | Equal | n lines | Pentagon, Hexagon, etc. |
Frequently Asked Questions
How do I calculate the area of an irregular shape?
For irregular shapes, you can often divide them into regular shapes (like triangles and rectangles), calculate each area separately, then sum them up. This is called the "composite shape" method.
What's the difference between perimeter and circumference?
Perimeter refers to the total distance around polygons (shapes with straight sides), while circumference specifically refers to the distance around a circle. Both measure the "outside length" but use different formulas.
Why do we use π in circle formulas?
π (pi) is the ratio of a circle's circumference to its diameter. This constant ratio (approximately 3.14159) appears in all circle calculations because it's fundamental to circular geometry.
How can I remember all these formulas?
Focus on understanding the logic behind formulas rather than memorization. For example, all area formulas essentially "fill" the shape with unit squares. Understanding why formulas work makes them easier to remember.
What's the most important shape in geometry?
While there's no single "most important" shape, triangles are fundamental because all polygons can be divided into triangles, and their properties form the basis of trigonometry. Circles are equally important for curved geometry.