AREA OF QUADRILATERAL

A plane figure bounded by four sides is known as a quadrilateral. The straight line joining the opposite corners is called its diagonal. The diagonal divides the quadrilateral in to two triangles.

Area of Quadrilateral General Formula

Let us derive the area of quadrilateral general formula. Consider the quadrilateral ABCD shown below :

We can observe the quadrilateral above as a combination of two triangles, considering the diagonal AC (or d) as common base. h1 and h2 are the heights of the two triangles.  

Area of quadrilateral ABCD above can be calculated by adding the areas of two two triangles ABC and ADC.

The area of quadrilateral ABCD is

= Area of Δ ABC + Area of Δ ADC

= 1/2 ⋅ d ⋅ h11/2 ⋅ d ⋅ h2

= 1/2 ⋅ d ⋅ (h1 + h2)

 Area of quadrilateral general formula : 

=   1/2

x

length of the diagonal

x

sum of the lengths of perpendiculars drawn to the diagonal

Here is the list of the formulas to find the area of quadrilaterals such as square, rectangle, parallelogram, trapezoid, kite and rhombus. 

Square

The area of a square is the product of the lengths of its two sides or square of the length of its diagonal. 

Area  =  s ⋅ s = s2

Area = 1/2 ⋅ d2

Rectangle

The area of a rectangle is the product of its base and height. 

Area  =  b ⋅ h

Parallelogram

The area of a parallelogram is the product of a base and its corresponding height. 

Area  =  b ⋅ h

Trapezoid (Trapezium)

The area of a trapezoid is one half the product of the height and sum of the bases. 

Area  =  1/2 ⋅ h ⋅ (b1 + b2)

Kite

The area of a kite is one half the product of the lengths of its diagonals. 

Area  =  1/2 ⋅ d1  d2

Rhombus

The area of a rhombus is one half the product of the lengths of its diagonals. 

Area  =  1/2 ⋅ d1  d2

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