Area of Quadrilateral
What is the area of a quadrilateral?
Area of the quadrilateral is the region inside the boundary of a quadrilateral. It is the total space occupied by a quadrilateral in 2-D plane. It is measured in square units.
How to find the area of a quadrilateral?
Area of quadrilateral is found using formula given below:
Area of Quadrilateral = (1/2) × [(x1y2 + x2y3 + x3y4 + x4y1) – (x2y1 + x3y2 + x4y3 + x1y4)]
where (x1, y1), (x2, y2), (x3, y3), and (x4, y4) are the vertices of a quadrilateral.
What are the different types of quadrilaterals?
Different types of quadrilateral are:
- Square
- Rectangle
- Rhombus
- Kite
- Parallelogram
- Trapezium
Write the uses of quadrilaterals.
Area of quadrilateral is used in the field of architecture, agriculture, design, and navigation also it helps to find distance between two points. It is required to find the area of buildings, park and other complexes.
How to calculate the area of a quadrilateral if one of its diagonals and both perpendiculars from the vertices are given?
When the diagonal(d) and the length of both perpendiculars (h, H) from the vertices are given, then the area of the quadrilateral is calculated by the formula:
Area of quadrilateral = (½) × d × (h + H)
What are the two main types of quadrilaterals?
The two main types of a quadrilateral are
- Regular Quadrilateral
- Irregular Quadrilateral
How to find the Area of a Quadrilateral using Heron’s Formula?
To find area of triangle using Heron’s Formula use the following steps:
- Step 1: Divide the quadrilateral in two triangles by joining its diagonal.
- Step 2: Find the area of both triangles using Heron’s formula.
- Step 3: Add both the areas to get the final answer.
Area of Quadrilateral
Area of Quadrilateral: The Area of a quadrilateral is the space inside the boundary of a quadrilateral or in other words, the space enclosed by the edges of a quadrilateral. A quadrilateral is a closed two-dimensional shape with four sides or edges, and also four corners or vertices. In mensuration, the shape of objects is classified based on the number of sides of the polygon.
The area of a quadrilateral can be found by dividing it into two triangles using a diagonal. When the length of the diagonal and the heights of the two triangles are given, the area of the quadrilateral is, A = (1/2) × Diagonal × (Sum of heights).
Quadrilaterals or any polygons can be classified into two categories, regular quadrilaterals/polygons i.e., all sides are of equal length, and irregular quadrilaterals i.e., all sides are not equal. This article explores the Area of Quadrilateral, using different methods, along with its formula, solved examples, and practice problems.
Table of Content
- What is a Quadrilateral?
- Properties of Quadrilateral
- What is the Area of Quadrilateral?
- Area of Quadrilateral Formula
- Area of Quadrilateral with Vertices
- Area of Quadrilateral Using Coordinates
- Area of Quadrilateral Using Area of Triangle
- Area of Quadrilateral Using Bretschneider′s Formula
- How to find the Area of Quadrilateral?
- Area of Some Quadrilaterals
- Area of a Square
- Area of a Rectangle
- Area of Rhombus
- Area of Parallelogram
- Area of Trapezium
- Area of Kite
- Area of Quadrilateral Solved Examples
- Practice Problems on Area of Quadrilateral
- Area of Quadrilateral Class 8