O square it is a convex polygon which has four sides. In other words, it is a flat geometric figure that has four congruent sides and four angles straight. In this way, it is also called quadrilateral.
You squares belong to a universe of geometric figures known as parallelograms. In this universe are also found the diamonds and rectangles, which, respectively, are defined as quadrilateral with congruent sides and quadrilateral with right angles.
In this way, all square it is also a rectangle, because every square has right inside angles, and it is also a diamond, because it has four congruent sides.
The figure used to represent the squares is as follows:
The square is a parallelogram
all square it's a parallelogram. This means that opposite sides of a square are parallel. In this way, the extensions of the opposite sides of a square any will never touch.
You squares inherit the properties of the parallelograms, which are as follows:
Opposite sides of a parallelogram are congruent;
Opposite angles of a parallelogram are congruent;
The adjacent angles of a parallelogram are supplementary, that is, their sum is equal to 180º;
any angle of a square measures 90°. Since the sum of adjacent angles is always 180° in the square, then regardless of the adjacent angles, they will be supplementary.
At diagonals of a parallelogram meet at their midpoints.
Therefore, the diagonals of the square they are also at their midpoints.
Properties and relationships in the square
You squares have a specific property inherited from the rectangle and the diamond:
In every square, diagonals are congruent and perpendicular.
The relationships that can be built are as follows:
Perimeter: can be calculated using the following formula:
P = 4.1
P is the perimeter and l is the length of the side of the square.
Area: can be calculated using the following formula:
A = 12
A is the area and l is the length of the side of the square.
Diagonal length: can be calculated by the following formula:
D = l·√2
By Luiz Paulo Moreira
Graduated in Mathematics
Source: Brazil School - https://brasilescola.uol.com.br/o-que-e/matematica/o-que-e-quadrado.htm