# Quadrilateral

A quadrilateral is a polygon with four sides (edges) and four vertices (corners). The word quadrilateral is made of the words quad (meaning four) and lateral (meaning sides). So, quadrilateral is simply a four sided figure.

The sum of interior angles for all quadrilaterals must be equal to 360 degrees.

### Types of Quadrilaterals

- Square
- Rectangle
- Parallelogram
- Rhombus
- Trapezoid

### Trapezium

When one pair of opposite sides is parallel and no condition for other pair of opposite sides, then the quadrilateral is trapezium.

When the non-parallel sides are equal in length then the trapezium formed is **isosceles trapezium**. The diagonals of isosceles trapezium are equal in length but do not bisect.

### Parallelogram

Opposite sides are equals and parallel. Opposite angles are equal. Diagonals bisect each other.

Each diagonal divides the parallelogram into two triangles of equal area.

Sum of any two adjacent angles is 180°.

### Rhombus

ll sides are equal, opposite sides are parallel. Opposite angles are equal.

Diagonals bisect each other at right-angled. But they are not equal. Each diagonal divides the rhombus into two triangles of equal area.

Area = 1/2 × d_{1} × d_{2}

### Rectangle

Pair of opposite sides equal. Each angle is 90°.

Diagonals are equal and bisect each other (not at right angles).

Length of diagonal = √(l^{2} + b^{2})

### Square

All sides are equal and angles equal.

Diagonals equal and bisect at 90°.

When it is inscribed in a circle, the diagonal of square is equal to the diameter of the circle. But when circle is inscribed in a square, the side of the square is equal to diameter of the circle.