Area of  a Quadrilateral

In this page area of a quadrilateral we are going to see how to find the area in mensuration. First let us see the formulas to be used to find the area of any quadrilateral then we are going to see example problems and their properties. 

Formula:

Area of quadrilateral = (1/2)  x d x (h₁ + h₂)

Here d -diagonal

h₁ & h₂ - perpendicular heights

Definition of quadrilateral:

The word quadrilateral can be separated as Quad + lateral. Here quad means four and lateral means sides. A shape which is having four sides is generally called quadrilateral. The shapes parallelogram, rectangle, square, rhombus and trapeziums are one of the type of quadrilateral.

Properties of quadrilateral:

• Sum of interior angles is 360°
• It has four sides
• It has four vertices 

Now we are going to some example problems based on these formulas

Example 1:

Find the area of a quadrilateral which is having the diagonal is measuring 50 m  and perpendicular height is measuring 10 m and 20 m

Solution:

Area of quadrilateral = (1/2)  x d x (h₁ + h₂)

Here h₁ = 10 m, h₂ = 20 m and d = 50 m

Area of quadrilateral = (1/2) x 50 x (10 + 20)

                            = (1/2) x 50 x 30

                            =  25 x 30  

                            = 750 m²

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Example 2:

Find the area of quadrilateral which is having the diagonal is measuring 20 m  and perpendicular height is measuring 5 m and 7 m

Solution:

Area of quadrilateral = (1/2)  x d x (h₁ + h₂)

Here h₁ = 5 m, h₂ = 7 m and d = 20 m

Area of quadrilateral = (1/2) x 20 x (5 + 7)

                            = (1/2) x 20 x 12

                            =  10 x 12  

                            = 120 m²

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Related Topics

• Perimeter of sector
  
• practice questions with solution
• Length of arc
• Practice questions on length of arc
  
• Perimeter of square 
• Perimeter of parallelogram
• Perimeter of rectangle
• Perimeter of triangle
• Area of a circle
• Area of Semicircle
• Area of Quadrant
  
• Area of sector
  
• Area of triangle
• Area of equilateral triangle
• Area of scalene triangle
  
• Area of square
  
• Area of rectangle
• Area of parallelogram
• Area of rhombus
• Area of trapezium
• Area around circle
• Area of pathways
• Area of combined shapes
  

Quote on Mathematics

“Mathematics, without this we can do nothing in our life. Each and everything around us is math.

Math is not only solving problems and finding solutions and it is also doing many things in our day to day life.  They are: 

It subtracts sadness and adds happiness in our life.    

It divides sorrow and multiplies forgiveness and love.

Some people would not be able accept that the subject Math is easy to understand. That is because; they are unable to realize how the life is complicated. The problems in the subject Math are easier to solve than the problems in our real life. When we people are able to solve all the problems in the complicated life, why can we not solve the simple math problems?

Many people think that the subject math is always complicated and it exists to make things from simple to complicate. But the real existence of the subject math is to make things from complicate to simple.”

Area of a Quadrilateral to Formulas for Shapes