Area of Quadrilateral Formula
In a quadrilateral ABCD, the length of the diagonal BD is ‘d’. ABCD can be divided into two triangles Δ ABD, and Δ BCD by the diagonal BD. For calculating the area of the quadrilateral ABCD we calculate the area of individual triangles and add them accordingly. But for calculating area of a triangle, its height must be known. Let us assume that the heights of the triangles ABD and BCD be h1 and h2 respectively.
Area of the triangle ABD = (1/2) × d × h1.
Area of the triangle BCD = (1/2) × d × h2.
From the figure, the area of the quadrilateral ABCD = area of ΔABD + area of ΔBCD.
Area of the quadrilateral ABCD = (1/2) × d × h1+ (1/2) × d × h2 = (1/2) × d ×( h1+h2 ).
Thus, the formula used to find the area of a quadrilateral is,
Area of Quadrilateral = (1/2) × Diagonal × (Sum of heights) = (1/2) × d ×( h1 + h2 )
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