Square

Definition

It is a geometric shape having four equal line segments that intersect at four points to create four internal angles of 90° each.

Properties

1. All four interior angles are right angles; in □ ABCD, ∠ABC = ∠BCD = ∠CDA =∠DAB =  90°
2. Has four vertices and four sides; A, B, C and D are vertices and AB, BC, CD and DA are sides
3. All four sides are congruent; so AB ≅ BC ≅ CD ≅DA
4. Opposite sides are parallel to each other; AB ∥ CD and BC ∥ DA
5. Diagonals of the square bisect each other at 90°
6. Two diagonals of the square are perpendicular to each other; AC = BD

Formulas

Diagonal

The segment that connects two opposite vertices of the square at right-angle to each other. The formula is given below:

Diagonal (d) = a × √2, here a = side length

Area

The total space enclosed by the square. The formula is given below:

Area (A) = a², here a = side length

Perimeter

The total distance covered around the edge of the square. The formula is given below:

Perimeter (P ) = 4a ,here a = side length

• More Resources
  • Area of Square
  • Perimeter of Square
  • Diagonal of Square
  • Vertices of a Square