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Types of Quadrilaterals, their properties, shapes, and areas
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Types of Quadrilaterals, their properties,
shapes, and areas
Quadrilateral properties, 6 types of quadrilateral, types of quadrilaterals chart, quadrilateral shapes, Trapezium, Parallelogram, Rectangle, Rhombus, Square, kite.
Family of Quadrilaterals
Trapezium:
If one pair of opposite sides of a quadrilateral is parallel then it is called a trapezium.
Properties of Trapezium
One pair of opposite sides are parallel.
Two pair of adjacent angles are supplementary.
Parallelogram:
If both pair of opposite sides of a quadrilateral is parallel then the quadrilateral is a parallelogram.
If one pair of opposite sides of a quadrilateral is equal and parallel then the quadrilateral is a parallelogram.
If both pair of opposite sides of a quadrilateral are equal and diagonals are not equal then the quadrilateral is a parallelogram.
Properties of parallelogram
 Opposite sides are equal and parallel.
 Opposite angles are equal.
 Adjacent angles are supplementary.
 Diagonals bisect each other.
 Diagonals are not equal.
 Area of parallelogram = Base x Height
Rectangle:
If one angle of a parallelogram is right then it is called a rectangle.
If both pair of opposite sides of a quadrilateral are equal and diagonals are also equal then the quadrilateral is a rectangle.
Properties of Rectangle Both pair of opposite sides are equal and parallel.
 Diagonals are equal and bisects each other.
 All angles are equal to 90^{o}
 Adjacent angles are supplementary.
Area of rectangle = Length X Breadth
Rhombus:
If adjacent sides of a parallelogram are equal then it is called a rhombus.If all sides of a quadrilateral are equal and diagonals are not equal then the quadrilateral is a rhombus.
Properties of Rhombus:
 All sides are equal.
 Opposite sides are equal and parallel.
 Opposite angles are equal.
 Adjacent angles are supplementary.
 Diagonals bisects each other at right angle.
 Diagonals are not equal.
 Area of Rhombus = Base x Height.
Square:
 All sides are equal.
 All angles are equal to 90^{o}
 Diagonal are equal.
 Adjacent angles are supplementary.
 Opposite side are equal and parallel.
 Opposite angles are equal.
 Perimeter of square is = 4 x side
 Area of Square is = (side x side)
A parallelogram whose one angle is right and adjacent sides are equal is called a square.
A rectangle whose adjacent sides are equal is called a square.
A rhombus whose one angle is right is called a square.
If all sides of a quadrilateral are equal and diagonals are also equal then the quadrilateral is a square.
Properties of Square
Type

Figure

Perimeter

Area

Quadrilateral

Sum of four sides


Trapezium

Sum of four sides


Parallelogram

Sum of four sides

Base x Height


Rectangle

2 (Length + Breadth)

Length x Breadth


Rhombus

4 x Side


Square

4 x Side


Kite

Sum of 4 sides

SPECIAL PROPERTIES OF QUADRILATERAL
 Quadrilateral
formed by joining the mid points of the sides of quadrilateral is called a parallelogram.
 Quadrilateral
formed by joining the mid points of the sides of a Parallelogram is called a Parallelogram.
 Quadrilateral
formed by joining the mid points of the sides of Rectangle is called a Rhombus.
 Quadrilateral
formed by joining the mid points of the sides of Rhombus is called a Rectangle.
 Quadrilateral formed by joining the mid points of the sides of Square is called a Square.
 Quadrilateral formed by joining the angle bisectors of opposite vertices of a parallelogram is called a Rectangle.
Polygons:
Closed figures with
sides three or more are called polygons.
Polygon with
three sides is called triangle.
Polygon with four
sides is called Quadrilateral.
Polygon with five
sides is called Pentagon.
Polygon with six sides
is called Hexagon.
Polygon with seven
sides is called Heptagon. and so on....
Measure of each interior angle of a polygon =
Measure of each exterior angle of a polygon =
Sum of all exterior angle of a polygon = 360^{o}
Number of diagonals of a polygon of side n is = or
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