What is an Area of Quadrilateral Mean By?
The 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 an area is, so that you can understand the concept of the area of the Quadrilateral.
Topics covered in this article
You will learn the following topics on this page.
1. Definition of area of a quadrilateral
2. Types of quadrilateral
3. How to calculate the area of a quadrilateral?
4. Properties of a quadrilateral
5. Formulas of the area of different types of quadrilateral
6. Solved examples of the area of a quadrilateral
7. 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:
Square
Rectangle
Parallelogram
Kite
Rhombus
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.
Every quadrilateral has four vertices, four sides, and four angles.
The sum of all the interior angles of a quadrilateral is always 360 degrees.
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.
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
How do you find the area of a quadrilateral?
Find the area of a parallelogram with base 10 m and height 12m?
Calculate the area of a kite having diagonals of length 13m and 10m?
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 quadrilaterals, SQUARE is the only regular quadrilateral; the rest all are irregular quadrilaterals.
The sum of all the angles of a quadrilateral is 360 degrees.
Key points on the area of quadrilateral
A Quadrilateral can be both of regular shape or irregular shape.
Some other examples of a Quadrilateral are Kite, rhombus and trapezoid.
The area of a quadrilateral is measured in square units like square metre, square centimetre etc.
FAQs on Area of Quadrilateral
1. What is an area of a quadrilateral where the coordinates of vertices are (1,2), (6,2), (5,3) and (3,4)?
The area of the quadrilateral will be 5.5 square units. To find this, a Quadrilateral ABCD will be drawn with a diagonal division and by adding the area of the two triangles ABC and ACD. For step by step solutions students can refer here.
2. 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.
