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Area of Quadrilaterals and Polygons

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Area of Quadrilaterals and Polygons - Lesson Summary

Triangle
Area of the triangle =   1 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 =  1 2 d (h 1 + h 2), where d is the diagonal and h 1 and h 2 are the heights of the quadrilateral.

Square
Area of the square = a 2 , 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 = l 2 + b 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 =   1 2  (d 1 x d 2), where d 1 and d 2 are the lengths of the diagonals.

Side of the rhombus = d 1 2 + d 2 2 2

Perimeter = 4 x (Side) = 2 . d 1 2 + d 2 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 d 1 x d 2
Trapezium
A trapezium has a pair of parallel sides.

Area of trapezium = h  (a + b ) 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.

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