A quadrilateral is any closed shape that has four sides. The sum of the measures of the angles is 360^{o}. Some of the known quadrilaterals are square,rectangle, trapezium, parallelogram and rhombus.

Quadrilaterals

### Square

A square is a regular quadrilateral that has four right angles and parallel lines. The diagonals also bisect each other perpendicularly.

**Properties**

If the side of the square is **a**, then its

- Perimeter = 4a
- Area = a
^{2} - Length of the diagonal = √2a

### Parallelogram

A parallelogram is a quadrilateral in which opposite sides are equal and parallel. Any two opposite sides of a parallelogram are called bases, a distance between them is called a height.

**Properties**

- Area of a parallelogram = base x height
- Perimeter = 2(Sum of two consecutive sides)
- Opposite sides of a parallelogram are equal
- Opposite angles of a parallelogram are equal
- Diagonals of a parallelogram are divided in their intersection point into two.
- The sum of square of diagonals is equal to the sum of squares of four sides AC
^{2}+BD^{2}=AB^{2}+BC^{2}+CD^{2}+AD^{2}

### Rectangle

A rectangle is a parallelogram with all its angles equal to right angles.

**Properties**

- Sides of the rectangle are its heights simultaneously.
- Diagonals of a rectangle are equal: AC = BD.
- Area of diagonals = length x breadth

### Rhombus

If all sides of a parallelogram are equal, then this parallelogram is called a rhombus.

**Properties**

- Diagonals of a rhombus are mutually perpendicular and divide its angles into two.
- Area of a rhombus is given by

### Trapezoid

A trapezium

A trapezoid is a quadrangle two opposite sides of which are parallel.

Here AD||BC, parallel sides are called bases of a trapezoid, the two others(AB and CD) are called lateral sides. A distance between bases(BM) is a height. The segment EF, joining midpoints E and F of the lateral sides, is called a midline of a trapezoid. A midline of a trapezoid is equal to half the sum of bases.

If AB = CD, the trapezoid is called an isosceles trapezoid.