POLIGONS
In geometry, a polygon can be dened as a flat or plane, two-dimensional closed shape bounded with straight sides. It does not have curved sides.
To find the sum of interior angles of a polygon, multiply the number of triangles in the polygon by 180°. The formula for calculating the sum of interior angles is
( n − 2 ) × 180 ∘ where is the number of sides.
Sum of angles of polygons
EXTERIOR ANGLES
Exterior angles of different polygons
Note:
The two outer angles at the same vertex are equal.
SUM OF EXTERIOR ANGLES
Note:
The sum of the outer angles of any polygon is 360˚.
REGULAR POLYGONS
REGULAR POLYGONS
For more detail, click here (youtube link1)
A polygon with equal sides and equal angles are called regular polygons.
NUMBER OF SIDES
Qn. Draw a regular hexagon
For answer, Click here (youtube link 2)
Qn. Calculate all sthe angle at the vertex D of regular pentagon ABCDE
Check your answer here (live video)
Points to be noted
THANK YOU
SQUARE
All sides are equal
Opposite sides parallel
All angles right
Diagonals equal
Diagonals perpendicular bisectors of each other
COSTRUCTION OF A SQUARE
Do you know how to construct a square using its diagonal length ?
The diagonal of an inscribed square is equal to the diameter of the circle. The diameter of the circle also divides the square into two equal right triangles.
Can you draw these patterns of squares in your note book ?
2cm
2cm
2cm
1.
2.
4cm
2cm
1cm
Solution
Check it .
3.
3.
A square is a quadrilateral.We made different types of pictures using this square! So Mathematics is also art
CONSTRUCTION OF QUADRILATERAL
Rectangle
IMAGES
YouTube video
Construct a rectangle when two adjacent sides are given�
• Draw a side of given length (say) CL ��• Draw side LU (say) of given length perpendicular to CL at L. ��• Draw side CE (say) of length equal to LU and perpendicular to CL at C. ��• Draw side UE.t C. ��• Draw side UE.
NOTES
TEXT WITH
HYPERLINK
How to construct rectangle in different ways?
Live video
PARALLELOGRAM
A parallelogram is a quadrilateral with two pairs of parallel sides. The opposite sides of a parallelogram are equal in length, and the opposite angles are equal in measure.
How to draw a parallelogram…
To know how to draw a parallelogram
Lets practice it more…
Here have a look at the problems of constructing parallelograms
TRAPEZIUM
A trapezium is a quadrilateral with exactly one pair of opposite sides parallel to each other
Properties of Trapezium
Construction of Trapezium
To know more about trapezium,
do
QUADRILATERALS
What is the common name of these shapes?
A quadrilateral is a plane figure that has four sides or edges , four angles and also has four corners or vertices.
Rectangle, square , parallelogram, rhombus, trapezium and isosceles trapezium are examples of quadrilaterals.
If you want to know more details about the features of quadrilateral, you can visit the link below
See the quadrilaterals
Two quadrilaterals may not be equal, even if all four sides are the same. Here the angle between two adjacent sides are different.
See the quadrilateral
In this quadrilateral length of three sides and two angles are given.
We can see the construction of this quadrilateral through the link given below.
For the construction of a quadrilateral atleast five measures are needed
In this quadrilateral length of three sides and two diagonals are given.
Watch the construction of this quadrilateral through the given link below.
Now we can draw a quadrilateral when length of four sides and one diagonal is given.
You can see the method of construction of this quadrilateral through the link given below
PARALLELOGRAM
Properties of parallelogram
Opposite sides are equal
Opposite sides are parallel
Diagonals bisects each other
Opposite angles are equal
A quadrilateral in which opposite sides are parallel and equal in length and opposite angles are equal in measure is called a parallelogram.
AREA OF PARALLELOGRAM
Do you know how to find the area of a parallelogram
The area of a parallelogram is the product of one side with the distance to the opposite side.
Can you find the area of these parallelogram in your notebook.
2.
1.
1. Area of parallelogram = SR * PT
= 5.6 * 3.7
= 20.72 cm
2
2. Area of parallelogram
= AD* CE
= 4 * 3
= 12 cm
2
Compute the area of the parallelogram given below
6 cm
3.5 cm
Area of parallelogram ABCD
= 2 ( ½ * 6 * 3.5 )
= 21 cm
2
Parallelogram is a quadrilateral in which opposite sides and angles are equal also opposite sides are parallel
The area of parallelogram is the product of one side of one side with the distance to opposite side.
To know more about parallelogram and to find the area of parallelogram
.
Properties of a Rhombus
What is my name…?
The diagonals of a rhombus splits it into four right triangles.
Let’s look at a rhombus with diagonals:
How can we find the area of a Rhombus?
The area of a rhombus is half the product of the diagonals.
AREA OF A RHOMBUS
Find the area of the Rhombus given below.
Check it out
Area of rhombus is 20 sq.cm.
The area of a Rhombus is 240 sq.cm and one of the diagonal is 16 cm. Find another diagonal.
Rhombus and Parallelogram are both quadrilaterals. What is the relation between area of both quadrilaterals?
ISOSCELES TRAPEZIUM
In Euclidean geometry, an isosceles trapezoid is a convex quadrilateral with a line of symmetry bisecting one pair of opposite sides. It is a special case of a trapezoid in which both legs and both base angles are of equal measure. The bases (the top and bottom) are parallel to each other. The angles on either side of the base are congruent. The angles on either side of the base are congruent.
AREA OF ISOSCELES TRAPEZIUM
To find area of isosceles trapezium,
A trapezium is a quadrilateral in which only one pair of opposite sides are parallel to each other. An isosceles trapezium is a trapezium in which the non-parallel sides are equal in measure.In an isosceles trapezium base angles are congruent where as it is need not be in the case of a trapezium
Only one pair of opposite sides parallel.
Sum of angles on each of non-parallel sides is supplementary.
Fix these shapes in the given trapezium by
dragging them
Name these shapes
click here to get the answer
Identify the figure with the given clues
Click here to get the solution
How to find the area of the trapezium?
4 cm
7 cm
3 cm
The lengths of the parallel sides of a trapezium are 30 centimetres, 10 centimetres and the distance between them is 20 centimetres. What is its area?
Solution :
1
2
24 cm
15 cm
7 cm
15 cm
15 cm
15 cm
24 cm
24 cm
3.Compute the area of the hexagon below
7 cm
4
Watch the video
TRAPEZIUM
BACK
TRIANGLES
BACK
QUADRILATERAL
INTRODUCTION
A quadrilateral is a polygon with four sides. It is a closed two dimensional figure formed by joining the four points among which three points are non-collinear points.It has four sides, four angles and four vertices.The sides of the quadrilateral may or may not equal.
EXAMPLES
GENERAL METHOD OF COMPUTING THE AREA OF QUADRILATERAL
The area of a quadrilateral is half the product of a diagonal and the sum of the perpendicular distances from the opposite vertices to this diagonal.
Area of general quadrilateral = ½×diagonal×(sum of height of two triangles)
T
T
Area of general quadrilateral
How to find area of a quadrilateral. Do check here
To know more about area of quadrilaterals,