Before knowing about the different types of the same let’s first understand about the basic shape. We know we obtain a line segment if all the points are collinear (in same line), we get a triangle if three out of four points are collinear, and we obtain a closed figure with four sides if none of the four points are collinear. The figures formed by joining such four non-collinear points in an order are called Quadrilaterals.
A quadrilateral is a 2-dimensional plane geometrical figure which has four sides, four angles, four vertices and two diagonals. The sum of all angles of a quadrilateral is 360 degree. Most of the object we see around us are of the shape of area of quadrilateral, like: blackboard, table, book, etc.
Properties of Quadrilaterals
- A quadrilateral should be a closed figure with 4 sides.
- All the internal angles of a quadrilateral sum up to 360 degrees.
Types and areas of quadrilaterals
There are basically six types of quadrilaterals.
Let’s discuss each of these six quadrilaterals in detail:
- Rectangle: *A quadrilateral with each of the four angles equal to right angles (90degrees) is called a rectangle.
* Moreover the opposite sides of a rectangle are always equal and parallel.
*Also the diagonals of a rectangle bisect each other.
Area of rectangle= length*breadth or L*B
- SQUARE: *A quadrilateral with all four sides equal and parallel to each other is called a square.
* Each of the angle of the square is 90 degrees and hence the sum of all the angles of a square is 360 degrees.
*The diagonals of a square bisects each other perpendicularly.
Area of the square = side^2= side*side
- Parallelogram:As the name itself suggests, a simple quadrilateral whose opposite sides are parallel is called a parallelogram. It has two pairs of parallel sides.
*Opposite angles are equal.
*Opposite sides are equal and parallel.
*Diagonals bisect each other.
*Sum of any two adjacent angles is 180 degrees.
Area of parallelogram=length*height, (when length and height are known)
*(the height is the perpendicular distance between parallel sides)
- Rhombus: A quadrilateral with all the four sides equal in length and opposite sides parallel to each other is a rhombus. But the angles are not equal to 90 degrees though the sum of the angles is 360
* Area of rhombus= ½*d1*d2 (where d1 and d2 are diagonal of a rhombus)
- Trapezium: A trapezium(trapezoid in U.S.) Is a type of quadrilateral which has only a pair of parallel sides which are referred to as bases and the other two sides are legs or lateral sides?
*Only one pair of opposite sides are parallel to each other.
*Area of trapezium=1/2* sum of parallel sides*height
- Kite: A quadrilateral with two adjacent sides equal is called a kite.
*Two pairs of adjacent sides of a kite are of same length.
*The larger diagonal bisect the smaller.
*only one pair of opposite angles arte of same measure.
*Area of kite=a*b*sin (a) where a is the angle between sides a and b
Apart from these 6 types, a quadrilateral can also be classified as:
- Concave quadrilaterals
- Convex quadrilaterals
- Intersecting quadrilaterals
- Cyclic quadrilaterals
Also we have regular quadrilaterals (all sides and angles equal) and irregular quadrilaterals (with all sides andangles unequal). These are very well explained by Cuemath and they the topic easy to understand.
Note- Areas are always expressed in square units (sq. unit). The S.I. unit of area is metersquare (m^2)
In EUCLIDEAN geometry, a quadrilateral is a polygon with four sides and four vertices.
We observed that
- Squares and rectangles are special types of parallelograms.
- A square is a special case of a rectangle and rhombus.
- A parallelogram is a trapezium.
- A kite is not a parallelogram.
- A trapezium is not a parallelogram.
- A rectangle or a rhombus is not a square.