## 12 Mar Square in Math

A square in math is a simple quadrilateral whose four sides all have the same length. It is a special type of rectangle in which both the length and breadth are equal in length. It is also a special type of rhombus that has an internal angle equal to 90 degrees.

The square has a perimeter length equal to 4 times the length of 1 of its side. Its area can be found by using the same formula as that of a rectangle which would be length multiplied by breath. In the case of a square, since the length and breadth have the same length, the formula for an area can also be re-written to be length squared.

A square has 4 lines of symmetry, 2 diagonally, which would split the square into two identical isosceles right angle triangles and 1 horizontal and 1 vertical which would split the square into rectangles.

The diagonals of a square bisect each other and meet at 90 degrees, they are also equal in length to each other. The opposite side of the square in math is parallel to each other. Other shapes that a square can be said to be a special case of includes parallelogram, kite, trapezium, and irregular 4 sided polygons and therefore has all the properties of all these shapes.

Characterizations of a square –

**A convex quadrilateral is a square if and only if it is any one of the following:**

- A rectangle with two adjacent equal sides
- A rhombus with a right vertex angle
- A rhombus with all angles equal
- A parallelogram with one right vertex angle and two adjacent equal sides
- A quadrilateral with four equal sides and four right angles
- A quadrilateral where the diagonals are equal and are the perpendicular bisectors of each other, i.e. a rhombus with equal diagonals
- A convex quadrilateral with successive sides a, b, c, d whose area is A = ½ (a^2 + c^2) = ½ (b^2 + d^2)

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