Square

In geometry, a square is a type of a regular quadrilateral. The lengths of the sides of the square are congruent in length and the opposite sides are parallel to each other. A Square consists of four vertices and the measure of all the angles are congruent. The diagonals of a square are perpendicular to each other. Diagonals are of the same length.

There are a number of properties of a square. Some of them are as follows:

• Diagonals of a square (quadrangle) bisect each other.
• Diagonals of a square (quadrangle) bisect its angles.
  
• Diagonals of a square (quadrangle) are perpendicular.
  
• Opposite sides of a square (quadrangle) are both parallel and equal.
  
• All four angles of a square (quadrangle) are equal. (Square is 360/4 = 90 degrees, so every angle of a square (quadrangle) is a right angle.)
  
• The diagonals of a square (quadrangle) are equal.

Perimeter of a Square is the total length of the boundary of the square. Since, all the sides of a square are of equal length and it has four sides, the perimeter of a square formula is,

Perimeter = 4 X side length

The perimeter of a square whose sides have length a is

Perimeter, P = 4a

The total space inside the boundary of the square is called as the area of a square. The area of a square is measured in terms of square units. The area of a square formula is,

Area, A = a²

Where, a is the length of the sides of the square.

In definitive times, the 2^nd power was stand for in terms of the area of a square, as in the above formulas. This led to the use of the terms square to mean increasing to the 2^nd power.

In the maximum (x², y²) = 1 is an equation of a square. The x² or y², is larger, equals 1. The `sqrt(2)` is circumradius of the square.

Below are some example problems on square

Example 1: Find the area of square pictures, whose side length is 15 ft

Solution:

The area of the square formula is, A = a²

Here, a is side length.

The side length, a = 15 ft

Area = 15²

Area = 15*15

Area of the square = 225 ft²

Answer = 225 ft²

Example 2: Find the area of square shape, whose side length is 9.5cm

Solution:

The area of the square formula is, A = a²

Here, a is side length.

The side length, a= 9.5cm

Area = (9.5)²

Area = 9.5 * 9.5

Area of the square = 90.25cm²

Answer = 90.25cm²

Example 3: Find the perimeter of square shape, whose side length is 7.8 m

Solution:

The perimeter of the square formula is, A = 4a

Here, a is the side length.

The side length, a = 7.8

Perimeter = 4 * 7.8

Perimeter = 31.2 m

Perimeter of the square = 31.2 m

Answer = 31.2 m