Calculating the Area of Quadrilaterals: Introduction and Examples

Calculating the Area of Quadrilaterals 390x220 1 - Calculating the Area of Quadrilaterals: Introduction and Examples

The area of a quadrilateral is the amount of area within it. Remember what a square is. A quadrilateral is a closed shape surrounded by four line segments. The squares can be regular or irregular. A regular quadrilateral is a square with all sides the same length. An irregular quadrilateral is called irregular squares. There are 6 types of quadrilateral:

  • Square 
  • Rectangle
  • Parallelogram 
  • Trapezoid
  • Rhombus 
  • Kite 

This article describes how to divide the area of a quadrilateral into two triangles and determine the area of a quadrilateral based on four sides and the area of quadrilateral formula. You will also learn formulas to find the regions of each of these different types of quadrilaterals.

Area a Quadrilateral: Introduction

The area of a square is just the area surrounded by the sides of the square. It is measured in square units such as m2, in2, and cm2. Determining the area of a quadrilateral depends on its type and the information available about the quadrilateral. If the rectangle is not of any of the above types, find it by splitting it into two triangles or using the formula (called the Bretschneider formula)  to find the area of the four-sided rectangle. The formula for finding a rectangular area that does not belong to any standard type is 1/2 x d x (h1 + h2).

Properties of Quadrilateral

  • Each quadrilateral has four corners and four sides, surrounding the four angles. 
  • The total internal angle is 360 degrees.  
  • Quadrilaterals usually have sides of various lengths and angles. However, squares, rectangles, parallelograms, etc., are special types of quadrilaterals with the same sides and angles.

Area formulas for all quadrilaterals

The formulas for the area of various types of rectangles such as squares, rectangles, rhombus, kites, parallelograms, trapezoids, etc. are shown below:

  1. Area of square = a2 square unit, where “a” is the length of one side of the square.  
  2. Rectangle area = l × b Square unit, where “l” and “b” are the length and width of the rectangle, respectively. 
  3. Area of parallelogram = w × h Square unit, where “b” and “h” are the length and height of the base of the parallelogram.
  4. Area of rhombus = (½) x d1 x d2 square unit, where “d1” and “d2” are the two diagonals of the diamond. 
  5. Kite area = (½) pq square units, where “p” and “q” are the two diagonals of the kite. 
  6. Trapezoidal area = (½) (a b) h square units, where “a” and “b” are the lengths of parallel sides, and “h” is the height of the trapezoid.
Quadrilateral Type Area Example
Square a x a = a2 where “a” is the length of one side. Let a= 5m, then area of a square is 5 x 5= 25m2
Rectangle Base x Height Let b=2 and h= 3, therefore area of rectangle is 2 x 3 =6m2
Parallelogram Base x Height Let b=4 and h= 6, therefore area of parallelogram is 4 x 6 =24m2
Kite ½ x Diagonal 1 x Diagonal 2 Let d1 = 18m and d2 = 10m, Area of a Kite = ½ x 16 x 10 = 90m
Rhombus Base x Height Let b = 4 m, h= 7 m, then Area of Rectangle = 4 x 7 = 28m2
Trapezium (a b)/2 x h, where a and b are opposite bases and h is the height. Let a = 4m, b= 8m and h = 2m, then Area of trapezium = (4 8)/2 x 2 = 12m2

Area of Quadrilateral: Examples

Example 1: Find the area of the rectangle whose length is 12 in and width is 16 in.

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Solution:

The length of the rectangle is l = 12 in.

Its breadth is, b = 16 in.

Using the formulas of the area of a quadrilateral, the area (A) of the given rectangle is,

A = l × b = 12 × 16 = 192 in2.

Answer: The area of the given rectangle = 192 in2.

Example 2: Find the area of a kite whose diagonals are 20 units and 16 units.

Solution:

The diagonals of the given kite are, d1 = 20 units and d2 = 16 units.

Using the formulas of the area of a quadrilateral, the area (A) of the given kite is,

A = (1/2) × d1 × d2 = (1/2) × 20 × 16 = 160 square units.

Answer: The area of the given kite = 160 square units

Conclusion

Hope this article helped you understand how to calculate the Area of Quadrilaterals.

Frequently Asked Question

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Q1. What are the different types of Quadrilaterals?

Ans. The different types of quadrilaterals are Rectangle, Rhombus, Square, Parallelogram, Kite, Trapezium.

Q2. How to calculate the area of the quadrilateral?

Ans. Quadrilaterals are a combination of basic geometric shapes called triangles. To calculate the area of a square, you need to calculate the area of each triangle and add the area of each triangle.