To show that the area of a parallelogram is equal to the product of its base and corresponding height by using paper cutting and pasting
Answers
Answer:
Objective
To show that the area of a parallelogram is equal to the product of its base and corresponding height by using paper cutting and pasting.
Prerequisite Knowledge
Construction of parallelogram by paper folding.
Area of rectangle = length x breadth
Area of parallelogram = base x corresponding height.
Materials Required
Glazed papers, pencil, a pair of scissors, gluestick.
Procedure
Draw a parallelogram by paper folding using coloured glazed paper and name it as ABCD.
Cut the parallelogram with the help of scissors.
In the parallelogram, draw a perpendicular from a vertex D to its opposite side AB of the parallelogram ABCD by paper folding.
We will get a crease along DE. Dark the colour in AADE [fig (i)]. Now cut it along DE. We will get two pieces, one triangle named as AED and other one a trapezium named E’D’CB as shown in fig.(ii).


Paste this triangular piece AED on the other side of trapezium such that its side AD coincides with BC [fig (iii)].

After pasting, we get a rectangle E’ECD’ with length as E’B + BE = E’E = D’C = AB and breadth as E’D’ = EC.
Observation
We observe that new figure D’E’EC is a rectangle.
Area of parallelogram ABCD = Area of rectangle E’ECD’
= length x breadth
= E’E x D’E’
= AB x DE
Hence, Area of parallelogram = Base x Height
Result
It is verified that the area of a parallelogram is equal to the product of its base and corresponding height by paper cutting and pasting method.
Learning Outcome
We can draw perpendicular from different vertices on opposite sides of parallelogram and verify that the area of the parallelogram is the product of base and height.
Area of parallelogram with the same base and the same height are identical. This leads to famous theorem:
“Parallelogram between the same parallel lines and on the same base are equal in area
Answer:
Step-by-step explanation:
Objective:- Area of a parallelogram = b*h
Materials Required:- A blank sheet of white paper, Some coloured papers, a pair of scissors and of course, a pen
Step 1:- Cut a parallelogram and name it as anything you like. I have named it as PQRS.
Step 2:- Draw perpendiculars from any point, say D to the opposite vertex P and do it on the either sides. Now cut it as shown in the picture attached.
Step 3:- Join both of the resultant triangles to form a square and join the square to the remaining part of the parallelogram to get a rectangle.
So, if we take the length of any of the sides as our base and the distance between them as the height or altitude, we can, by using the area for a rectangle (l*b) as the area of the parallelogram (b*h).
Hence proved, area of parallelogram= B*H
