Notes On Area of Quadrilaterals and Polygons - CBSE Class 8 Maths
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 = , 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 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. #### Summary

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 = , 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 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. Next