Area of Quadrilaterals and Polygons
We can find the area of the triangle using the formula 
To find the area of a quadrilateral we will 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)
= ½ d (
), where d is the diagonal and 
and 
are the heights of the quadrilateral.Area of quadrilateral ABCD= ½ d (
) 
In a parallelogram the diagonal divide it into two triangles. Now
Area of a Parallelogram = base × height
Area of a Parallelogram = base × height
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 =
(
), where 
and 
are the lengths of the diagonals.
Area of a Rhombus =
(
), where 
and 
are the lengths of the diagonals.A trapezium has a pair of parallel sides.
Area of trapezium =
Where h = perpendicular distance between the parallel sides of a trapezium and a and b are the lengths of the parallel sides.
Area of trapezium =
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.
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