Home » Maths » What is Quadrilateral? Definition, Properties & Example

# What is Quadrilateral? Definition, Properties & Example

A quadrilateral is a polygon with four sides, four vertices (corners), and four angles. It is also known as a quadrangle or tetragon.  The quadrilateral is derived from two words, ‘quadri‘ which means four, and ‘lateral‘ which means side.

1. Sum of Interior Angles: The sum of the interior angles of a quadrilateral is always 360 degrees.
2. Diagonals: A diagonal is a line segment connecting two non-adjacent vertices of a quadrilateral. The number of diagonals in a quadrilateral is equal to half of the product of its sides minus two.
3. Area: The area of a quadrilateral can be found by using different formulas based on its type.
4. Perimeter: The perimeter of a quadrilateral is the sum of its four sides.

1. Parallelogram
2. Rectangle
3. Rhombus
4. Square
5. Trapezium
6. Kite

Quadrilaterals can be classified into different types based on their properties and characteristics. ### 1. Parallelogram

A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are congruent and parallel to each other. The opposite angles of a parallelogram are also congruent. In other words a quadrilateral is a parallelogram if

• its opposite sides are equal.
• opposite angles are equal.
• its diagonals bisect each other.
• it has one pair of opposite sides parallel and equal.

### 2. Rectangle

A rectangle is a parallelogram with four right angles. The opposite sides of a rectangle are congruent and parallel to each other. A rectangle properties are:

• opposite sides are equal.
• each angle is a right angle.
• diagonals are equal.
• diagonals bisect each other.

### 3. Rhombus

A rhombus is a parallelogram with four congruent sides. The opposite angles of a rhombus are congruent. A rhombus properties are:

• all sides are equal.
• opposite angles are equal.
• diagonals bisect each other at a right angle.

### 4. Square

A square is a rectangle with four congruent sides. It has four right angles and is a regular quadrilateral. A square properties are:

• all the sides are equal.
• each angle is a right angle.
• diagonals are equal.
• diagonals bisect each other at a right angle.

### 5. Trapezium

A trapezoid is a quadrilateral with at least one pair of parallel sides. The non-parallel sides are called legs and the parallel sides are called bases. A trapezium properties are:

• one pair of opposite sides is parallel.
• interior angles on the same side of each of the non-parallel sides are supplementary.

### 6. Kite

• two pairs of adjacent sides are equal and opposite sides are unequal.
• diagonals intersect each other at right angles.
• the diagonals bisects the other diagonal.
• only one pair of opposite angles is equal. ### Quadrilateral examples in real life

We can see the shape of quadrilaterals in several objects around us, like in a deck of cards, a chessboard, a kite, a tub of popcorn, and an arrow. The formula for finding the area of a quadrilateral depends on the type of quadrilateral. Here are the formulas for some common types of quadrilaterals: Square Area = s2
Rectangle Area = l x w
Parallelogram Area = b x h
Rhombus Area = (d1 x d2) / 2
Trapezoid Area = ((b1 + b2) / 2) x h

Note:

• “s” represents the length of a side in a square
• “l” represents the length and “w” represents the width of a rectangle
• “b” represents the length of the base and “h” represents the height of a parallelogram and trapezoid
• d1 and d2 represent the length of the diagonals of a rhombus
• In a trapezoid, b1 and b2 represent the lengths of the parallel bases, and “h” represents the height or perpendicular distance between the bases.

Example1: If the side length of a square is 5 cm, find the area of Square.

Area = s2

= 52

area of Square = 25 square cm

##### Example2: If the length of a rectangle is 8 cm and the width is 4 cm, then find the area of Rectangle.

Area = l x w

= 8 x 4

the area of Rectangle = 32 square cm

Example3: If the base of a parallelogram is 10 cm and the height is 6 cm, then find the area of Parallelogram.

Area = b x h

= 10 x 6

area of Parallelogram = 60 square cm

Example4: If the diagonals of a rhombus are 6 cm and 8 cm, then find the area of Rhombus.

Area = (d1 x d2) / 2

= (6 x 8) / 2

the area of Rhombus  = 24 square cm

Example5: If the two parallel bases of a trapezoid are 6 cm and 10 cm, and the height is 8 cm, then find the area Trapezoid.

Area = ((b1 + b2) / 2) x h

= ((6 + 10) / 2) x 8

the area Trapezoid  = 64 square cm

error: