Area of Quadrilateral Formula: Definition, Types, Properties

The Area of Quadrilateral Formula represents the space enclosed by the four sides of this polygon. The standard formula for calculating the area of a quadrilateral is base multiplied by height, denoted as b * h, with the unit of measurement in square meters (m²). Quadrilaterals can be categorized into two main types: regular and irregular. In the following discussion, you will acquire the knowledge required to determine the area of any type of quadrilateral, whether it's a square or a trapezium. To start, let's establish a clear understanding of what area signifies, thereby laying the foundation for comprehending the concept of the area of a quadrilateral.

Definition of Area of Quadrilateral Formula

The concept of the area of a quadrilateral can be defined as follows: An area represents a specific region enclosed within the boundaries or sides of a particular geometric figure. When this figure possesses four sides, the region enclosed by these four sides is referred to as the area of a quadrilateral. The measurement unit for the area of a quadrilateral is typically in square units, with the standard unit being square meters, often denoted as m².

Area of Different Types of Quadrilateral

There are various types of quadrilaterals, including but not limited to:

• Square
• Rectangle
• Parallelogram
• Kite
• Rhombus
• Trapezium

Each of these quadrilaterals has unique properties and formulas for calculating their respective areas.

How to Calculate the Area of a Quadrilateral?

Step 1: Begin by creating a diagonal PR, connecting the opposite vertices of the quadrilateral PQRS.

Step 2: Extend a perpendicular line from each of the vertices (P, Q, R, and S) to intersect the diagonal PR.

Step 3: To find the area of quadrilateral PQRS, you can divide it into two triangles, namely △PQR and △PRS.

Therefore, the area of quadrilateral PQRS is determined by the sum of the areas of these two triangles: (½ * PR * PT) + (½ * PR * RU), where T and U represent the points where the perpendiculars from vertices P and R intersect diagonal PR.

What are the Properties of a Quadrilateral?

A quadrilateral is defined by its four vertices, four sides, and four angles.

The total of all the interior angles within a quadrilateral always equals 360 degrees.

The lengths of the four sides of a quadrilateral can vary; they may be equal in some cases, like the sides of a square, or unequal in others, such as those of a trapezium.

Also Check – Derivatives Formula

Area Formulas of Different Types of Quadrilaterals

Square:

If 's' is the length of one side of the square, then the area (A) is given by:

A = s ²

Rectangle:

If 'l' is the length and 'w' is the width of the rectangle, then the area (A) is given by:

A = l * w

Parallelogram:

If 'b' is the length of the base and 'h' is the height (perpendicular distance between the bases), then the area (A) is given by:

A = b * h

Kite:

If 'd1' and 'd2' are the lengths of the two diagonals of the kite, then the area (A) is given by:

A = (1/2) * d1 * d2

Rhombus:

If 'd1' and 'd2' are the lengths of the diagonals of the rhombus, then the area (A) is given by:

A = (1/2) * d1 * d2

Trapezium (Trapezoid):

If 'a' and 'b' are the lengths of the parallel sides, and 'h' is the height (distance between the parallel sides), then the area (A) is given by:

A = (1/2) * (a + b) * h

These are the standard area formulas for different types of quadrilaterals, each tailored to the specific characteristics of the shape.

Also Check – Factors and Multiples Formula

Solved Examples of Area of Quadrilateral Formula

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

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

Solution: To find the area of the quadrilateral, we can use the formula: Area = ½ * (Sum of parallel sides) * Height

Given:

a = 60 m

b = 20 m

h = 50 m

Substituting the values into the formula:

Area = ½ * (60 + 20) * 50

Area = ½ * 80 * 50

Area = 40 * 50

Area = 2000 m²

Example 2: A quadrilateral has four sides, each measuring 4 cm in length. Determine its area.

Solution: A quadrilateral with all sides of equal length is a square. The area of a square is given by the formula: Area = side^2, where 'side' is the length of one side of the square.

Given:

Side length (a) = 4 cm

Area = 4 cm * 4 cm

Area = 16 cm²

Example 3: The length of a quadrilateral (rectangle) is 6 m, and the width is 5 m. Calculate the area of this rectangle.

Solution: The area of a rectangle is given by the formula: Area = length * width.

Given:

Length (l) = 6 m

Width (b) = 5 m

Area = 6 m * 5 m

Area = 30 m²

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

Solution: The area of a kite is calculated using the formula: Area = ½ * (Diagonal 1) * (Diagonal 2).

Given:

Diagonal 1 (d1) = 6 m

Diagonal 2 (d2) = 8 m

Area = ½ * 6 m * 8 m

Area = 24 m²

Example 5: A rectangle has sides measuring 5 m and 10 m. Determine the area of this rectangle.

Solution: The area of a rectangle is calculated as Area = length * width.

Given:

Length (l) = 5 m

Width (b) = 10 m

Area = 5 m * 10 m

Area = 50 m²

These examples illustrate how to calculate the area of different quadrilaterals using their specific formulas and given measurements.

Also Check – Integer Formula

Key Points on the Area of Quadrilateral

A quadrilateral can take on either a regular or irregular shape.

Other examples of quadrilaterals include the kite, rhombus, and trapezoid.

The measurement unit for the area of a quadrilateral is typically in square units, such as square meters or square centimeters.