Explore the perfect symmetry and properties of squares. Learn formulas, understand relationships with other quadrilaterals, and discover symmetry principles.
A square is a parallelogram where all four sides are equal and all four angles are right angles (90°). It's the most regular and symmetric of all quadrilaterals.
Squares combine the properties of rectangles (right angles) and rhombuses (equal sides), making them special cases of both shapes.
All sides same length
Each angle is 90°
Perpendicular & bisecting
Maximum symmetry
P = 4a
Where a is the side length
Example: Square with side 6 → P = 4 × 6 = 24 units
A = a²
Where a is the side length
Example: Square with side 6 → A = 6² = 36 square units
Squares have the highest degree of symmetry among all quadrilaterals, making them perfectly balanced shapes.
Two diagonal lines and two lines through midpoints of opposite sides
Looks identical when rotated 90°, 180°, 270°, and 360°
The intersection of diagonals is the center of symmetry
A square is a special case of several other quadrilaterals. Understanding these relationships helps classify shapes correctly.
When length = width
Every square is a rectangle, but not every rectangle is a square
When angles = 90°
Every square is a rhombus with right angles
When all sides equal and all angles = 90°
Every square is a parallelogram with additional constraints
Chess board squares demonstrate perfect square properties with equal sides and right angles, creating a fair playing field.
Square sticky notes are designed for maximum writing space while maintaining compact, stackable form.
Square ceramic tiles allow seamless fitting without gaps, creating stable and aesthetically pleasing floors.
Test your understanding with interactive square calculators and problem-solving tools.
Explore more quadrilateral shapes and their unique properties.