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Area of a Quadrilateral - Characteristics, Steps, Types, Examples and different types of quadrilateral Formulas Table

 

What is a Quadrilateral?

A quadrilateral is a polygon of four sides with an internal angle total of 360 degrees.

What are the Characteristics of a Quadrilateral?

Below listed are some standard yet important properties of quadrilateral:

  • Four vertices, four sides, and four angles are present in each quadrilateral.
  • The total of all quadrilateral inner angles is always 360 degrees.
  • The lengths may not always be equal for all four sides of the quadrilateral. For instance, a square's sides are similar, but not all four sides of a trapezoid are alike.

Steps to Determine the Area of a Quadrilateral

The area of any quadrilateral can be measured using the following three steps:

Step 1: Construct a diagonal AC that will connect the two opposite vertices of a quadrilateral ABCD.

Step 2: Draw a perpendicular line on the diagonal AC from the vertices B and D. The heights of each triangle are these perpendicular lines.

Step 3: Area of the quadrilateral ABCD = Area of △ABC + Area of △ACD. Therefore, the area of quadrilateral ABCD = (½ × AC × BK) + (½ × AC× DL), here K and L are the diagonal perpendiculars drawn from B and D vertices.

Different Types of Quadrilaterals

Fundamentally, there are six different types of quadrilaterals in this world. We encounter them in our day-to-day life. With different physical states as well as properties, the six distinct quadrilaterals are mentioned below:

  1. Square
  2. Rectangle
  3. Parallelogram
  4. Kite
  5. Rhombus
  6. Trapezium

Formulas to calculate the area of different types of Quadrilateral

The formula for finding the area of different quadrilaterals is also varied. Therefore, let us study the formulas in a tabular manner to find the area of different types of quadrilateral.

Quadrilateral Area Example
Square s×s = s2, where s is the length of each side of the square Let s= 5 m, then Area of square = 5×5 =25 m2
Rectangle Length (l) × Breadth (b) Let b = 3 m, l= 10 m, then Area of Rectangle = 3 × 10 = 30m2
Parallelogram Base (b) × Perpendicular Height (h) Let b = 2 m, h= 6 m, then Area of Parallelogram = 2 × 6 = 12m2
Kite ½ ×D1×D2, where D1 and D2 are the diagonals of the kite Let D1 = 20m and D2 = 12m, Area of a Kite = ½× 20× 12 = 120m2
Rhombus ½ × Product lengths of the diagonal (d1 X d2) Let d1 = 7 m, d2= 3 m, then Area of rhombus = 7 × 3 = 21m2
Trapezium (k + l)/2 × d, where k and l are lengths of the parallel sides of a trapezium and d is the perpendicular distance between the parallel sides. Let k = 5m, l= 11m and d = 2m, then Area of trapezium = (5+11)/2×2 = 4m2
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