Maths

# Square Properties With Examples A square is a two-dimensional plane shape having four equal sides and all four angles equal to 90 degrees, according to geometry. The features of a rectangle are similar to those of a square, however, the difference is that a rectangle only has equal opposite sides. As a result, a rectangle is only considered a square if all four sides are the same length.

### Definition of Square

The square is a polygon with four equal sides ( quadrilateral ). Its four interior angles are also equal and straight (90º each).

### Parts of Square

• Sides: the square has four sides ( a ) equal and parallels two to two.
• Angles: it has four equal and right angles (α) of 90º (π/2 radians). The interior angles, as in all quadrilaterals, add up to 360º (2π radians).
• Diagonals – Diagonals are segments joining opposite vertices. It has two equal and perpendicular diagonals ( 1 and 2 ). They intersect in the center of the square. The diagonals are the bisectors of the angles. They are also lines of symmetry.
• Symmetry axes are imaginary lines that divide the square into two symmetrical parts with respect to said axis. It has four axes of symmetry ( 123, and 4 ).

The square is a particular case of the rectangle, the pairs of sides being equal. It is also a particular case of the rhombus, with pairs of equal and right angles (90º).

### Square Shape

A square is a four-sided polygon with all four sides equal in length and all angles measuring 90 degrees. The square’s shape is such that if a plane is sliced through it from the center, both parts are symmetrical. Each half of the square now resembles a rectangle with equal sides on both sides.

## Square Properties

The following are the most important properties of a square:

• Each of the four inside angles is 90 degrees.
• The square’s four sides are congruent or equivalent to one another.
• The square’s opposite sides are parallel to each other.
• The square’s diagonals are 90 degrees apart and bisect each other.
• The square’s two diagonals are equal in length.
• The square has four sides and four vertices.
• The square’s diagonal divides it into two identical isosceles triangles.
• The length of the diagonals exceeds the length of the square’s sides.

### How to find Area and Perimeter of Square?

The area and perimeter are the two fundamental characteristics that distinguish a square from other shapes. Let’s have a look at them one by one:

### Area of Square

The area of the square is the region enclosed by it in a two-dimensional plane. The area of the square here is equal to the square of the sides. It is measured in square units.

Area = side2 per square unit

If ‘x’ is the length of the side of the square, then;

Area = x2 sq.unit

### Perimeter of Square

The square’s perimeter is equal to the sum of its four sides. The perimeter is measured in the same unit as the square’s side length.

Perimeter = Side + Side + Side + Side = 4 Side

Perimeter = 4 × side of the square

If ‘x’ is the length of the side of the square, then the perimeter is:

Perimeter = 4x unit

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