Math Playground
Geometry

Square

Rectangle with all sides equal — and four lines of symmetry.

A square is the all-rounder: four equal sides and four right angles. It's a rectangle (right angles), a rhombus (equal sides) and a parallelogram all at once — the most symmetric quadrilateral there is.

Drag the corners
10101010
square
area ≈ 100.0 sq units
Area & perimeter

Diagonal length = s√2 ≈ 1.414 s.

Square symmetry & diagonals

  • 4 lines of symmetry (2 through opposite sides, 2 through opposite corners) and rotational symmetry of order 4.
  • The two diagonals are equal, bisect each other, and meet at 90°.
  • Each diagonal splits the square into two congruent right isosceles triangles.
  • Among all rectangles with a given perimeter, the square has the biggest area.
Your turn

A square has area 49 cm². What is its perimeter, and how long is its diagonal?