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
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?