## Square

In this tutorial, we will learn about the Geometric shape, Square. We shall learn its properties and some special things that involve square.

Square is a special case of Geometric shape, quadrilateral, in which all four sides are equal in length and all four angles are equal.

Following is a picture of a square.

Let us give some naming to the vertices of this square and we shall use these names to understand the properties of a square in more detailed manner.

Like any quadrilateral, Square has four vertices (or corners), four sides (or edges), four angles (at four vertices) and two diagonals. Following table gives a detailed overview about a square.

Property | Values | Information |

Vertices | A, B, C, D | |

Sides | AB, BC. CD, DA | AB = BC = CD = DA |

Angles | ∠A, ∠B, ∠C, ∠D | ∠A = ∠B = ∠C = ∠D = 90° |

Diagonals | AC, BD | AC = BD |

### What do you need to define or draw a square?

All you need is length of a side to define or draw a square.

Hence, properties like perimeter, area, etc., depend only on the length of side.

### How to draw a square?

For example, consider that we need to draw a square whose length of a side is 4cm.

**Step 1:** Draw a line segment AB of length 4cm.

**Step 2:** Draw a line segment BC, of length 4cm, perpendicular to AB. Line segments AB and BC should touch at B.

**Step 3:** Draw a line segment CD, of length, perpendicular to BC and parallel to AB. Line segments CD and BC should touch at C.

**Step 4:** Join vertices A and D with line segment. The distance between A and D would be 4cm, if you followed step 1 through step 3 correctly.

The plane area enclosing these four line segments AB, BC. CD. DA is our square with side length of 4cm.

### Property 1: All sides of a square are equal in length

All the sides of a square are equal. If a side is of length `a`

units, then rest of the three sides also have the same length `a`

units.

### Property 2: All angles of a square are equal

All the four angles of a square are equal, and equal to 90 degrees.

### Property 3: Diagonals are equal in length

Diagonals are straight line segments joining opposite vertices. In a square, length of diagonals are equal.

Each diagonal bisects square into two equal halves along the opposite vertices.

### Perimeter of Square

As all the sides are equal in a square and as there are four sides, the perimeter of square equals four times the length of a side in the square.

### Area of Square

The area enclosed in square is side length times side length.

In the following diagram, we have taken a square of length 4 units. The area is the number of square units present.

### Summary

In this tutorial, we learned how to define a Square, how to draw a Square and different properties of a square.