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Area of General Quadrilateral

Quadrilateral

A Quadrilateral is a polygon which has four sides and four vertices. It is a two dimensional closed shape with four straight sides. A line segment joining the opposite vertices is called a diagonal of the quadrilateral. A general quadrilateral can be split into two triangles by drawing one of its diagonals.

 

The diagram shown above is the quadrilateral ABCD, and the line segment joining the opposite vertices (ie) A and C is the diagonal of the quadrilateral ABCD. By drawing the diagonal we can split the quadrilateral into two triangles. By this triangulation we can find the area of the quadrilateral.
 

Area of the quadrilateral:

 

 
Example

Find the area of quadrilateral PQRS.

Solution

Here

d = 6.5 cm, h1 = 3.5 cm, h2 = 4.5 cm

Area of PQRS

                  


Special types of Quadrilateral:

Rhombus

Rhombus is a special type of quadrilateral where all the four sides are equal in length. Opposite sides of rhombus are parallel to each other. The diagonals of the rhombus bisect each other.

 

Here are some examples of rhombus.
 

 
 

Area of rhombus:

Consider a rhombus ABCD. Draw diagonals AC and BD. The diagonals of rhombus bisect each other perpendicularly. Area of the rhombus can be found out by the method of splitting into triangles.

Area of rhombus ABCD = (area of D ACD) + (area of D ABC).

Where AC =

d1, BD = d2.

Area of rhombus is half the product of its diagonals.
 

Example

Find the area of a rhombus whose diagonals are of lengths 5
cm and 4.2 cm.

Solution

Area of rhombus

          

 

Example:

Find the area of the pendent which is in the shape of rhombus. The diagonals of the rhombus are 4.5 cm and 5.6 cm.

Solution:

 





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