In geometry, the term Polygon is used to describe a two dimensional closed shape made of straight lines segments. Polygons can be of different types depending on the number of sides.
What is a Quadrilateral?
A quadrilateral is a polygon with 4 sides and 4 vertices. The word quadrilateral is derived from the Latin words - quadri and latus which mean 4 and sides respectively.
Types of quadrilaterals
Quadrilaterals can be of two types - simple and complex. A Simple quadrilateral is not self-intersecting and its interior angles always add up to 360°.
Simple
Simple quadrilaterals can be further classified as convex or concave.
Simple - Convex
In a convex quadrilateral, all interior angles are less than 180° and its two diagonals lie inside the quadrilateral (Diagonal is the line segment that connects the opposite vertices of the quadrilateral). Examples of convex quadrilateral are square, rectangle, rhombus, trapezium. Square and rectangle have equal and perpendicular diagonals.
Square: All sides of a square are equal and every angle is a right angle. Opposite sides are parallel to each other. Area of a square = a2 where a is the length of the side.
Rectangle: Opposite sides are equal and parallel to each other. All angles are right angles. Area of a rectangle = l * b where l is the length and b is the breadth of the rectangle.
Rhombus: All sides have equal length. The diagonals of a rhombus bisect each other at right angles. Sometimes a rhombus is also referred to as a diamond.
Parallelogram: Opposite sides are equal in length and parallel to each other. Opposite angles of a parallelogram are of equal measure.
Simple - Concave
In a concave quadrilateral, one interior angle is greater than 180° and one of the two diagonals lies outside the quadrilateral.
Type of quadrilateral |
Equal diagonals |
Bisecting diagonals |
Perpendicular diagonals |
Square |
Yes |
Yes |
Yes |
Rectangle |
Yes |
Yes |
No |
Rhombus |
No |
Yes |
Yes |
Parallelogram |
No |
Yes |
No |
Complex
Complex quadrilaterals are self-intersecting i.e. two of the sides of the quadrilateral cross over each other. The point at which they cross over does not create an additional pair of vertices, hence a complex quadrilateral also has 4 sides and 4 vertices.
Practice questions:
Question: Calculate the area of a square of size 4 cms.
(Answer: Area of the square = 4 * 4 = 16 sq cms
)
Question: Calculate the area of a rectangle of length 4 cms and breadth 2 cms.
(Answer: Area of the rectangle = 4 * 2 = 8 sq cms.
)
Question: Given that the area of a square is 9 sq cms, what is the length of its side?
(Answer: Area of the square = x * x = 9
X = 3 cms
)
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