Quadrilaterals: an introduction

What are quadrilaterals?
A quadrilateral is a plane figure bounded by four line segments such that:
(a) No two line segments cross each other, and
(b) No two line segments are collinear.
In simple words, a four sided closed two dimensional figure is called a quadrilateral.

Types of quadrilaterals:

The next question that comes to our mind is what is a quadrilateral shape? There are various types of quadrilaterals whose description is given below:
(i) A quadrilateral with both pairs of opposite sides parallel is called a parallelogram.
(ii) A quadrilateral with exactly one pair of parallel sides is called a trapezium or a trapezoid. An isosceles trapezium  is a trapezium in which two non parallel sides are equal.
(iii) A kite is a quadrilateral in which two pairs of adjacent sides are equal.
(iv) A parallelogram in which all angles are right angles is called a rectangle.
(v) A parallelogram in which all sides are equal is called a rhombus
(vi) A rectangle with all sides equal, or a rhombus in which all angles are right angles is called a square.

Properties of quadrilaterals:
1. All quadrilaterals have four sides. The word quadrilateral itself means ‘four sided’.
2. Since all quadrilaterals have four sides, it is obvious that it would have four angles as well.
3. All sides are straight.
4. The figure has to be two dimensional.
5. The sum of interior angles of a quadrilateral is always 360 degrees.

Area of a quadrilateral:

The area of quadrilateral formula depends on the type of quadrilateral we have. Let us look at the formulae for area of various types of quadrilaterals:

1. Parallelogram: Area = length of base * perpendicular distance between the two bases
2. Trapezoid: Area = (1/2) * sum of parallel sides * perpendicular distance between the parallel sides
3. Kite: Area = area of upper triangle + area of lower triangle, where area of triangle = (1/2) * base * height.
4. Rectangle: Area = length * width
5. Rhombus: Area = (1/2) * product of the diagonals
6. Square: Area = (side)^2.
If a quadrilateral is none of the above, then to find the area we split the quadrilateral into two triangles. Find the area of both the triangles and add them up, to give the area of the quadrilateral. Alternatively if we know the co-ordinates of the vertices of a quadrilateral also we can find the area using co-ordinate geometry.