Quadrilaterals for all classes
In Geometry, the shapes or objects are classified based on the number of sides. The different classification of shapes are:
- Triangle ( 3-sides)
- Quadrilateral (4-sides)
- Pentagon (5-sides)
- Hexagon (6-sides)
- Heptagon (7-sides)
- Octagon (8-sides) and so on.
In this article, we are going to discuss “Quadrilaterals” in detail.
Quadrilateral Definition
A quadrilateral is a plane figure that has four sides or edges, and also has four corners or vertices. Quadrilaterals will typically be of standard shapes with four sides like rectangle, square, trapezoid, and kite or irregular and uncharacterized as shown below:
Types of Quadrilaterals
There are many types of quadrilaterals. As the word ‘Quad’ means four, all these types of a quadrilateral have four sides, and the sum of angles of these shapes is 360 degrees.
- Trapezium
- Parallelogram
- Squares
- Rectangle
- Rhombus
- Kite
Another way to classify the types of quadrilaterals are:
- Convex Quadrilaterals: Both the diagonals of a quadrilateral are completely contained within a figure.
- Concave Quadrilaterals: At least one of the diagonals lies partly are entirely outside of the figure.
- Intersecting Quadrilaterals: Intersecting quadrilaterals are not simple quadrilaterals in which the pair of non-adjacent sides intersect. This kind of quadrilaterals are known as self-intersecting or crossed quadrilaterals
Quadrilateral Formula
The area of the quadrilateral is the total space occupied by the figure. The area formula for the different quadrilaterals are given below:
| Area of a Parallelogram | Base x Height |
| Area of a Rectangle | Length x Width |
| Area of a Square | Side x Side |
| Area of a Rhombus | (1/2) x Diagonal 1 x Diagonal 2 |
| Area of a Kite | 1/2 x Diagonal 1 x Diagonal 2 |
Perimeter of Quadrilateral
Perimeter is the total distance covered by the boundary of a 2d shape. Since we know the quadrilateral has four sides, therefore, the perimeter of any quadrilateral will be equal to the sum of the length of all four sides. If ABCD is a quadrilateral then, the perimeter of ABCD is:
Perimeter = AB + BC + CD + AD
| Quadrilateral Name | Perimeter |
| Square | 4 x Side |
| Rectangle | 2(Length + Breadth) |
| Parallelogram | 2(Base + Side) |
| Rhombus | 4 x Side |
| Kite | 2 (a + b), a, and b are adjacent pairs |
Quadrilateral Properties
Let us understand in a better way with the help of an example:
- Four sides: AB, BC, CD, and DA
- Four vertices: Points A, B, C, and D
- Four angles: ∠ABC, ∠BCD, ∠CDA, and ∠DAB
- ∠A and ∠B are adjacent angles
- ∠A and ∠C are the opposite angles
- AB and CD are the opposite sides
- AB and BC are the adjacent sides
A quadrilateral is a 4-sided plane figure. Below are some important properties of quadrilaterals :
- Every quadrilateral has 4 vertices, 4 angles, and 4 sides
- The total of its interior angles = 360 degrees
Square Properties
- All the sides of the square are of equal measure
- The sides are parallel to each other
- All the interior angles of a square are at 90 degrees (i.e., right angle)
- The diagonals of a square perpendicular bisect each other
Rectangle Properties
- The opposite sides of a rectangle are of equal length
- The opposite sides are parallel to each other
- All the interior angles of a rectangle are at 90 degrees.
- The diagonals of a rectangle bisect each other.
Rhombus Properties
- All the four sides of a rhombus are of the same measure
- The opposite sides of the rhombus are parallel to each other
- The opposite angles are of the same measure
- The sum of any two adjacent angles of a rhombus is equal to 180 degrees
- The diagonals perpendicularly bisect each other
Parallelogram Properties
- The opposite side of the parallelogram are of the same length
- The opposite sides are parallel to each other
- The diagonals of a parallelogram bisect each other
- The opposite angles are of equal measure
- The sum of two adjacent angles of a parallelogram is equal to 180 degrees
Properties of Trapezium
- Only one pair of the opposite side of a trapezium is parallel to each other
- The two adjacent sides of a trapezium are supplementary (180 degrees)
- The diagonals of a trapezium bisect each other in the same ratio
Properties of Kite
- The pair of adjacent sides of a kite are of the same length
- The largest diagonal of a kite bisect the smallest diagonal
- Only one pair of opposite angles are of the same measure.
Summary of Quadrilateral Properties
| Square | Rectangle | Rhombus | Parallelogram | Trapezium | |
| All sides are equal | Yes | No | Yes | No | No |
| Opposite sides are parallel | Yes | Yes | Yes | Yes | Yes |
| Opposite sides are equal | Yes | Yes | Yes | Yes | No |
| All the angles are of the same measure | Yes | Yes | No | No | No |
| Opposite angles are of equal measure | Yes | Yes | Yes | Yes | No |
| Diagonals bisect each other | Yes | Yes | Yes | Yes | No |
| Two adjacent angles are supplementary | Yes | Yes | Yes | Yes | No |
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