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.