Area of Quadrilateral

Area of the quadrilateral is the region enclosed by the four sides of this polygon. The general formula of the area of a quadrilateral is base * height, also written as b*h and the unit of measurement is m2. There are two types of quadrilaterals - regular and irregular. On this page, you will learn how to find the area of any type of quadrilateral, be it a square or a trapezium. Let’s first understand what is an area, so that you can understand the concept of the area of the Quadrilateral. You will learn the following topics on this page.

  • Definition of area of a quadrilateral

  • Types of quadrilateral

  • How to calculate the area of a quadrilateral?

  • Properties of a quadrilateral

  • Formulas of area of different types of quadrilateral

  • Solved examples of area of a quadrilateral

  • Practice Questions 

Definition of Area of Quadrilateral

An area is defined as any region which is included in a particular boundary or figure. If that figure has four sides, the region inside these four sides will be called an area of a quadrilateral. The area of a quadrilateral is measured in square units. The standard unit for measuring an area is mainly square metres, also written as m2.

Area of Different Types of Quadrilateral

As explained in the above paragraph, any polygon having four sides is a quadrilateral, so we have many types of quadrilaterals. Some of them are:

  1. Square

  2. Rectangle

  3. Parallelogram

  4. Kite

  5. Rhombus

  6. Trapezium


How to Calculate the Area of a Quadrilateral?

Step 1: Construct a diagonal PR that will join the opposite vertices of the quadrilateral PQRS.

Step 2: From each of these vertices, draw a perpendicular on the diagonal PR.

Step 3: Area of the quadrilateral PQRS = Area of △PQR + Area of △PRS

Therefore, area of quadrilateral PQRS = ( ½ * PR * PT) + (½ * PR * RU), where T and U are the perpendiculars from the vertices P and R on the diagonal.


What are the Properties of a Quadrilateral?

Let’s learn the basic properties of a quadrilateral.

  1. Every quadrilateral has four vertices, four sides, and four angles.

  2. The sum of all the interior angles of a quadrilateral is always 360 degrees.

  3. The lengths of all the four sides of a quadrilateral may or may not be equal. For example, the sides of a square are equal but all the four sides of a trapezium are not equal.

Area Formulas of Different Types of Quadrilaterals

As the lengths of the four sides of a quadrilateral may or may not be equal, the formulas to find their areas are also different. Let us learn the formulas to find the area of all the types of quadrilateral in a tabular form.

Quadrilateral Type

Area

Example

Square

a * a = a2, where a is the length of the side of the square.

Let a = 4 m, then Area of square = 4*4 =16 m2

Rectangle

Base * Height or (b * h)

Let b = 2 m, h= 4 m, then Area of Rectangle = 2 * 4 = 8m2

Parallelogram

Base * Height or (b * h)

Let b = 4 m, h= 5 m, then Area of Rectangle = 4 * 5 = 20m2

Kite

½ * Diagonal 1*Diagonal 2

Let d1 = 16m and d2 = 10m, Area of a Kite = ½*16*10 = 80m2

Rhombus

Base * Height or (b * h)

Let b = 3 m, h= 6 m, then Area of Rectangle = 3 * 6 = 18m2

Trapezium

(a+b)/2 * h, where a and b are opposite bases and h is the height.

Let a = 2m, b= 4m and h = 3m, then Area of trapezium = (2+4)/2*3 = 9m2


Solved Examples of Area of Quadrilateral

Example 1 : Calculate the area of a quadrilateral with the given measurements:

Diagonal = 50 m, Perpendicular height = 60 m and 20 m.

Solution: Area of quadrilateral = ½ * (a+b) * h

Given : a = 60 m , b = 20 m and h = 50 m

Substituting the values in the formula we get,

A = ½ *(60+20) * 50 

    = ½ * 80 *50

    = 40 * 50

    = 2000 m2


Example 2: A quadrilateral has four equal sides each of length 4cm. Find its area?

Solution: A quadrilateral of all sides equal is known as Square. 

Area of a square - a 2, where a is the side of the square.

A = 4m * 4m = 16m2

Example 3: The length of a quadrilateral (rectangle) is 6 m and the breadth is 5m. What would be the area of this rectangle?

Solution: Area of a rectangle  = l *b

Given : l = 6m and b = 5m

Area of a rectangle = 6m * 5m = 30m2

Example 4: A quadrilateral in the shape of a kite has two diagonals of length 6 m and 8 m. Find the area of this quadrilateral?

Solution: Area of a kite = ½ *1d1 *d2

Given : d1 = 6m and d2  = 8m

A = ½ *  6m * 8m = 24m2

Example 5: A rectangle has sides of length of 5 m and 10 m, Find the area of this rectangle?

Solution: Area of Rectangle = length * Breadth

Given: l = 5m and b = 10m

A = 5m * 10m = 50m2

Now that you know what is the area of a quadrilateral and how to find it, it’s time you should practice the given questions to test your knowledge.


Practice Questions on Quadrilaterals

  1. How do you find the area of a quadrilateral?

  2. Find the area of a parallelogram with base 10m and height 12m?

  3. Calculate the area of a kite having diagonals of length 13m and 10m?

  4. Which one is not a quadrilateral - triangle, square, rectangle?

Did You Know?

  • In the word Quadrilateral, Quad means Four and Lateral means sides.

  • In all types of quadrilateral, SQUARE is the only regular quadrilateral, rest all are irregular quadrilaterals.

  • The sum of all the angles of a quadrilateral is 360 degrees.