Area Samralab Ldh
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Govt. Sen. Sec. School Samrala Presentation on Parallelogram and Its Area
Made By Taranjeet Singh Yashandeep Singh Kuldeep Singh Mrinaal
Guided BY Jatinder Saddi (Math Teacher) Anjali Manro(CF)
Source of Information:P.S.Ed.B. Text Book of 7TH & 8TH
INDEX 1) What is Parallelogram? 2) Properties of the Parallelogram. 3) Area of parallelogram (Definition) 4) Area of parallelogram (Formula) 5) Derivation of the formula.
WHAT IS A PARALLELOGRAM ? Parallelogram:A quadrilateral in which opposite sides are parallel is called a parallelogram. As a result, its opposite sides are also equal. .
Quadrilateral ABCD is a parallelogram because AB|| DC and AD||BC.
PROPERTIES OF THE PARALLELOGRAM Properties:1)
2)
3)
In a parallelogram opposite sides are equal, i.e. in parallelogram ABCD, AB=CD and AD=BC. In a parallelogram, opposite angles are equal, i.e. in parallelogram ABCD, ∠A=∠C and ∠B=∠D. The diagonals of a parallelogram are bisectors of each other, i.e. in parallelogram AO=OC and BO=OD.
AREA OF PARALLELOGRAM Area of parallelogram:The plane enclosed by the perimeter of the parallelogram is called its area.
The coloured portion shown in the figure represents the area of the parallelogram ABCD
AREA OF PARALLELOGRAM We find the area of the parallelogram by the multiplication of one of its side and perpendicular drawn on it. Area of Parallelogram = One Side × Perpendicular drawn on it
DERIVATION OF THE FORMULA 1) Draw a parallelogram ABCD. 2) Draw BE⊥AB or DC, Cut it along BE.
3) Place side BC of the cut part on AD; because opposite sides of a parallelogram are equal, therefore BC will be covered by AD completely i.e. point A will coincide with B and D with C while E will coincide E′.
4)
Thus we get a new figure –a rectangle ABEE′.
We know, Area of Rectangle = Length × Breadth Therefore area of rectangle ABEE′ = AB × BE This is equal to the area of original parallelogram ABCD. Thus area of parallelogram ABCD = AB × BE As we know AB is one of the sides of parallelogram ABCD and BE is the perpendicular drawn on it. Therefore we can also write the above relation as:Area of a parallelogram = One side × Perpendicular drawn on it
Made By Taranjeet Singh Yashandeep Singh Kuldeep Singh Mrinaal
Guided BY Jatinder Saddi (Math Teacher) Anjali Manro(CF)
Source of Information:P.S.Ed.B. Text Book of 7TH & 8TH
INDEX 1) What is Parallelogram? 2) Properties of the Parallelogram. 3) Area of parallelogram (Definition) 4) Area of parallelogram (Formula) 5) Derivation of the formula.
WHAT IS A PARALLELOGRAM ? Parallelogram:A quadrilateral in which opposite sides are parallel is called a parallelogram. As a result, its opposite sides are also equal. .
Quadrilateral ABCD is a parallelogram because AB|| DC and AD||BC.
PROPERTIES OF THE PARALLELOGRAM Properties:1)
2)
3)
In a parallelogram opposite sides are equal, i.e. in parallelogram ABCD, AB=CD and AD=BC. In a parallelogram, opposite angles are equal, i.e. in parallelogram ABCD, ∠A=∠C and ∠B=∠D. The diagonals of a parallelogram are bisectors of each other, i.e. in parallelogram AO=OC and BO=OD.
AREA OF PARALLELOGRAM Area of parallelogram:The plane enclosed by the perimeter of the parallelogram is called its area.
The coloured portion shown in the figure represents the area of the parallelogram ABCD
AREA OF PARALLELOGRAM We find the area of the parallelogram by the multiplication of one of its side and perpendicular drawn on it. Area of Parallelogram = One Side × Perpendicular drawn on it
DERIVATION OF THE FORMULA 1) Draw a parallelogram ABCD. 2) Draw BE⊥AB or DC, Cut it along BE.
3) Place side BC of the cut part on AD; because opposite sides of a parallelogram are equal, therefore BC will be covered by AD completely i.e. point A will coincide with B and D with C while E will coincide E′.
4)
Thus we get a new figure –a rectangle ABEE′.
We know, Area of Rectangle = Length × Breadth Therefore area of rectangle ABEE′ = AB × BE This is equal to the area of original parallelogram ABCD. Thus area of parallelogram ABCD = AB × BE As we know AB is one of the sides of parallelogram ABCD and BE is the perpendicular drawn on it. Therefore we can also write the above relation as:Area of a parallelogram = One side × Perpendicular drawn on it
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