QUADRILATERAL

 Quadrilateral  

Quadrilateral

A quadrilateral is a closed shape and a type of polygon that has four sides, four vertices and four angles. It is formed by joining four non-collinear points. The sum of interior angles of quadrilaterals is always equal to 360 degrees. 

The polygon has four vertices or corners.

 

We can find the shape of quadrilaterals in various things around us, like in a chess board, a deck of cards, a kite, a tub of popcorn, a sign board and in an arrow.

 

 

Types of Quadrilaterals

The types of quadrilaterals are defined based on the measure of the angles and lengths of their sides. 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. The list of types of quadrilaterals are:

1. Trapezium

2. Parallelogram

3. Squares

4. Rectangle

5. Rhombus

6. Kite

   

 Name of the Quadrilateral: Properties of the Quadrilateral:

 Parallelogram Opposite sides are parallel.

 Opposites sides are equal.

 Opposite angles are equal.

 Square All sides are equal.

 All angles are equal and measure 90°.

 Rectangle Opposite sides are parallel.

 Opposites sides are equal.

 All angles are equal and measure 90°.

 Rhombus All sides are equal.

 Opposite angles are equal.

 Trapezoid Opposite sides are parallel.

 Adjacent angles add up to 180°.

 

Properties of Quadrilaterals

 

• It has four sides: AB, BC, CD, and DA

• It has four vertices: Points A, B, C, and D

• It has 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 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

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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

Click here to learn the definition and formulas related to trapezium.

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.

Quadrilaterals Solved Examples

Example 1: What is the base of a rhombus, if its area is 40 square units and the height is 8 units?

Solution:

Given,

Area = 40 square units

Height = 8 units

Area of rhombus = Base × Height

40 = Base × 8

Base = 40/8 = 5 units

Example 2: If 15 metres and 6 metres are diagonal lengths of a  kite, then what is its area?

Solution: Given, diagonal 1 = 15 metre and diagonal 2 = 6 metre. So, the area is simply calculated as, (1/2)(15×6) = 45 m2.

Example 3: Find the perimeter of the quadrilateral with sides 5 cm, 7 cm, 9 cm and 11 cm.

Solution: Given, sides of a quadrilateral are 5 cm, 7 cm, 9 cm and 11 cm.

Therefore, perimeter of quadrilateral is:

P =  5 cm + 7 cm + 9 cm + 11 cm = 32 cm

Example 4: The perimeter of the quadrilateral is 50 cm and the lengths of the three sides are 9 cm, 13 cm and 17 cm. Find the missing side of the quadrilateral.

Solution: Let the unknown side of the quadrilateral = x

Given, Perimeter of the quadrilateral = 50 cm

The lengths of other three sides are 9 cm, 13 cm and 17 cm

As we know,

Perimeter = sum of all the four sides.

50 = 9 cm + 13 cm + 17 cm + x

50 = 39 + x

x = 50 – 39

x = 11

Therefore, the fourth side of quadrilateral = 11 cm

How many of these quadrilateral facts do you know?

• A quadrilateral is a two-dimensional geometric shape. 
• A quadrilateral has 4 sides.
• A quadrilateral has four straight sides. 
• A quadrilateral has four vertices. 
• There are six special quadrilaterals: square, rectangle, parallelogram, rhombus, trapezium, and kite. 
• A quadrilateral is a polygon. 

Types of quadrilaterals

Square 

How many of these square facts do you know?

• A square is a two-dimensional geometric shape. 
• A square has 4 sides.
• A square has four straight sides. 
• A square’s sides are all the same length. 
• A square’s opposite sides are parallel.
• A square has four vertices. 
• A square’s vertices are all the same size. The vertices are all 90º. 
• All squares are rectangles but not all rectangles are squares.
• The sum of all the angles of a square is 360º. 90º + 90º + 90º + 90º = 360º
• A square is a polygon. 

Rectangle

How many of these rectangle facts do you know?

• A rectangle is a two-dimensional geometric shape. 
• A rectangle has 4 sides.
• A rectangle has four straight sides. 
• A rectangle has two sets of sides that are the same length. 
• A rectangle’s opposite sides are parallel.
• A rectangle has four vertices. 
• A rectangle’s vertices are all the same size. The vertices are all 90º. 
• The sum of all the angles of a rectangle is 360º. 90º + 90º + 90º + 90º = 360º
• A rectangle is a polygon. 

 

Kite 

How many of these kite facts do you know?

• A kite is a two-dimensional geometric shape. 
• A kite has 4 sides.
• A kite has four straight sides. 
• A kite has two pairs of sides that are the same length. 
• A kite has four vertices. 
• A kite has one pair of equal angles. 
• A kite is a polygon. 

Rhombus 

How many of these rhombus facts do you know?

• A rhombus is a two-dimensional geometric shape. 
• A rhombus has 4 sides.
• A rhombus has four straight sides. 
• A rhombus has two pairs of sides that are the same length. 
• A rhombus’ opposite sides are parallel.
• A rhombus has four vertices. 
• A rhombus has two pairs of equal angles. 
• Lines drawn joining the opposite angles of a rhombus bisect each other at right angles. 
• A rhombus is a polygon. 

Parallelogram 

How many of these parallelogram facts do you know?

• A parallelogram is a two-dimensional geometric shape. 
• A parallelogram has 4 sides.
• A parallelogram has four straight sides. 
• A parallelogram has two pairs of sides that are the same length. 
• A parallelogram’s opposite sides are parallel.
• A parallelogram has four vertices. 
• A parallelogram has two pairs of angles that are all the same size. 
• Lines drawn joining the opposite angles of a parallelogram bisect each other. 
• A parallelogram is a polygon. 

Trapezium

How many of these trapezium facts do you know?

• A trapezium is a two-dimensional geometric shape. 
• A trapezium has 4 sides.
• A trapezium has four straight sides. 
• A trapezium has one pair of parallel sides.
• A trapezium has four vertices. 
• A trapezium is a polygon. 
• A trapezium is sometimes called a trapezoid.