### CBSE Assignments class 09 Mathematics

Mathematics Assignments & Worksheets  For  Class IX Chapter-wise mathematics assignment for class 09. Important and useful extra questions strictly according to the CBSE syllabus and pattern with answer key CBSE Mathematics is a very good platform for the students and is contain the assignments for the students from 9 th  to 12 th  standard.  Here students can find very useful content which is very helpful to handle final examinations effectively.  For better understanding of the topic students should revise NCERT book with all examples and then start solving the chapter-wise assignments.  These assignments cover all the topics and are strictly according to the CBSE syllabus.  With the help of these assignments students can easily achieve the examination level and  can reach at the maximum height. Class 09 Mathematics    Assignment Case Study Based Questions Class IX

### Types of Quadrilaterals, their properties, shapes, and areas

Types of Quadrilaterals, their  properties, shapes, and areas

Any closed figure bounded by four sides is called a quadrilateral. A quadrilateral has four sides four vertices and four angles.

A quadrilateral have 4 sides, 4 vertices and 4 angles.
Sum of all angles of a quadrilateral is 360

$Area\: of\: quadrilateral\: =\frac{1}{2}\times AC(DE+BF)$
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.
$Area\: of\: trapezium=\frac{1}{2}\times (b_{1}+b_{2})\times h$

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.
• 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  90o
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.
• Diagonals  bisects each other at right angle.
• Diagonals are not equal.
• Area of Rhombus = Base x Height.
• $Area\: of\: Rhombus\: =\frac{1}{2}\times Product\: of\: diagonals$
• $Area\: of\: Rhombus\: =\frac{1}{2}\times d_{1}\times d_{2}$
Square:-
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

• All sides are equal.
• All angles are equal to 90o
• Diagonal are equal.
• Opposite side are equal and parallel.
• Opposite angles are equal.
• Perimeter of square is = 4 x side
• Area of Square is = (side x side)
• $Area\: of\: Square\: =\frac{1}{2}\times d_{1}\times d_{2}$
• $Area\: of\: Square\: =\frac{1}{2}\times product\: of\:diagonals$

Kite

If two pair of adjacent sides of a quadrilateral is equal then the quadrilateral is a kite.

### Properties of Kite

• Two pairs of adjacent sides are equal.
• Diagonals are perpendicular to each other.
• One diagonal bisect the other.
• $Area\: of\: kite\: =\frac{1}{2}\times d_{1}\times d_{2}$

 Type Figure Perimeter Area Quadrilateral Sum of four sides $\frac{1}{2}\times AC[DE+BF]$ Trapezium Sum of four sides $\frac{1}{2}\times (b_{1}+b_{2})\times h$ Parallelogram Sum of four sides Base x Height Rectangle 2 (Length + Breadth) Length x Breadth Rhombus 4 x Side $\frac{1}{2}\times d_{1}\times d_{2}$ Square 4 x Side $=side\times side\\\\ \: \:\: \: \: \: =\frac{1}{2}\times d_{1}\times d_{2}$ Kite Sum of 4 sides $\frac{1}{2}\times d_{1}\times d_{2}$

• 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....

Sum of all interior angles of a polygon is given by the formula = (n-2) X 180.

Measure of each interior angle of a polygon = $\left ( \frac{n-2}{n} \right )\times 180^{o}$

Measure of each exterior angle of a polygon  =  $\frac{360^{o}}{n}$

Sum of all exterior angle of a polygon = 360o

Number of diagonals of a polygon of side n is =  $\frac{n^{2}-3n}{2}$  or  $\frac{n(n-1)}{2}-n$