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Square

A square is defined as a two-dimensional figure that is which is surrounded by four lines. It comes under the category of quadrilaterals which have four sides. A square is bounded by four equal sides that are joined together at right angles. An image showing square is given below:

Square

Squares are of great importance in geometry. They are everywhere in real life. A chess board and a carom board are square, a photo frame may be square, a cushion may be square in shape etc.

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Properties of a Square

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Square possesses properties as mentioned below:
  • A square has 4 sides, 4 vertices and 2 diagonals.
  • All four sides of a square are equal.
  • Opposite sides of a square are parallel.
  • All four interior angles are $90^{\circ}$.
  • The diagonals of a square are equal in length.
  • Both diagonals bisect each other at right angles.
  • A square is a type of rhombus where all angles are $90^{\circ}$.

Diagonal of a Square

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Diagonal of a square can be derived using Pythagorean theorem:
If the side of square is denoted by "a", then diagonal

$d^{2} = a^{2} + a^{2}$

$d^{2} = 2 a^{2}$
d = a $\sqrt{2}$

Perimeter of a Square

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Perimeter of a square is the sum of all four sides. Since all the sides have same measure (say "a"), hence perimeter is given by:
Perimeter of square = 4 $\times$ side = 4 a

Area of a Square

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Formula for the area of a square of side "a" is:
Area of square = side $\times$ side = side$^{2}$ = a$^{2}$

Examples

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Example 1: Find the area and perimeter of the square whose side length is 8 meters.

Solution:

Given that:

$a = 8m$

Area of square = $a^2 = 8 \times 8 = 64 m^2$

Perimeter of the square = $8 \times 8 = 64 m$

Example 2: Each side of a square is 6.5 cm. Find its perimeter.

Solution: Side = $6.5 cm$

Therefore, perimeter of a square = $4 \times length \ of \ a \ side$

                                            = $(4 \times 6.5) cm$

                                            = $26 cm$



More topics in  Square
Area of Square
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