Area of Quadrilaterals and Polygons

Triangle
Area of the triangle =  $\frac{\text{1}}{\text{2}}$ x base x height.

Quadrilateral
To find the area of a quadrilateral divide the quadrilateral into two triangles and add the areas of the two triangles. The method of dividing a quadrilateral into two triangles to find out its area is known as triangulation.

Let ABCD is a quadrilateral.

Then Area of quadrilateral ABCD = (Area of ∆ ABD) + (Area of ∆ BCD)

Area of quadrilateral ABCD = $\frac{\text{1}}{\text{2}}$d (h₁ + h₂), where d is the diagonal and h₁ and h₂ are the heights of the quadrilateral.

Square
Area of the square = a² , where a be the length of each side of a square.

Perimeter of square = 4a.

Diagonal of a square = √2a

Rectangle

Area = length x breadth

Perimeter = 2( length + breadth)

Diagonal = $\sqrt{{\text{l}}^{\text{2}}\text{+}{\text{b}}^{\text{2 }}}$, where l = length b = breadth.



Parallelogram
In a parallelogram the diagonal divide it into two triangles. 

Area of a Parallelogram = base × height

Perimeter = 2( Sum of two adjacent sides)



Rhombus
In a rhombus diagonals are perpendicular to each other, so we can use the method of triangulation to find the area of a rhombus.

Area of a Rhombus =  $\frac{\text{1}}{\text{2}}$ (d₁ x d₂), where d₁ and d₂ are the lengths of the diagonals.

Side of the rhombus = $\frac{\sqrt{{{\text{d}}_{\text{1}}}^{\text{2}}\text{+}{{\text{d}}_{\text{2}}}^{\text{2}}}}{\text{2}}$

Perimeter = 4 x (Side) = 2$\sqrt{{}_{\text{.}}{{\text{d}}_{\text{1}}}^{\text{2}}\text{+}{{\text{d}}_{\text{2}}}^{\text{2}}}$



Area of rhombus DEFG = (½ x EO x DF) + (½ x GO x DF)
                                              = ½ x DF x (DF + GO)
                                              = ½ x DF x GE
                                              = ½ x d₁ x d₂
Trapezium
A trapezium has a pair of parallel sides.

Area of trapezium = h $\frac{\text{(a + b )}}{\text{2}}$

Where h = perpendicular distance between the parallel sides of a trapezium and a and b are the lengths of the parallel sides.



A polygon is a closed shape that has at least three sides. It is a closed shape that has at least three sides. Triangles, quadrilaterals, rectangles and squares are all types of polygons. Moreover, a polygon can be of any shape and can have any number of sides. There is no specific formula for calculating the area of a polygon. The best way is to split the polygon into shapes whose area can be calculated individually.