Question

What is the area of quadrilateral when all sides are given?

Answer 1

when it is a quadrilateral we should check how many sides

for example square: s x s

                  rectangle : L X B

AND WE HAVE TO CHECK THE FORMAL

Answer 2

The sum of two any two triangles formed by its diagonal gives the area of a quadrilateral. There are 6 types of quadrilateral and its area can be found only when its sides are given.

The types of quadrilaterals are:

1. Square: quadri

When the lengths of all four sides are equal, the lateral becomes square.  

Area of a square ABCD=$a^2$

2. Rectangle:

When the lengths of the parallel sides are equal, the quadrilateral becomes rectangle. When rectangle is divided into two triangles, the angle between the adjacent sides are right angle.

Area of a rectangle ABCD=a×b  

3. Parallelogram:

When the opposite sides are equal and parallel, the quadrilateral becomes parallelogram.  

Area of parallelogram ABCD=base×height  

Area of parallelogram ABCD=base×height×$sin\ \sin \theta$   (when angle of the diagonal is included)

4. Rhombus:

When the sides are equal and diagonals are unequal, then the quadrilateral becomes Rhombus.

Area of rhombus ABCD=$a^2\ sin\ sin \theta$   (When one angle is included)

Area of rhombus ABCD=$\frac 12(product\ of\ two\ diagonals)$ (when two angles are included)

5. Trapezoid:

When two sides are parallel and other two sides are non-parallel, then the quadrilateral becomes trapezoid.  

Area of trapezoid=$\frac{Sum\ of\ parallel\ sides}2*height$

6. Cyclic quadrilateral:

When the four edges of quadrilateral are on circumference of a circle, then it is called as cyclic quadrilateral.

Area of cyclic quadrilateral=2S=a+b+c+d