Area of parallelogram

As performed in the real lab:

Materials Required:

Glazed paper, pencil, a pair of scissors, gum.

Procedure:

1. Make a parallelogram by paper folding. Call it ABCD.
2. Cut out the parallelogram with the help of a pair of scissors.
3. Obtain a perpendicular from D to AB meeting AB at E. [Fig A]
4. Cut and remove the triangle AED and align AD with BC. Call the displaced segment AE as BE'. [Fig B]
5. Verify using a scale that EBE' are collinear.
6. Verify that CE' is perpendicular to EBE and EE' = CD
7. Observe that the figure obtained is a rectangle.[Fig B]

 


As performed in the simulator:

  1. Create a parallelogram ABCD with length L and breadth B.[Fig C]
  2. Draw perpendicular from A to DC meeting at point E.
    1.     Click on "Set Square" in Tools to use it.
    2.     Drag and place Set Square such that point A and line DC is perpendicular.
  3. Click on ▲ AED to separate it from parallelogram.
  4. Drag ▲ AED and place it such a way that AD is overlapped with BC.
  5. Please see the observation

Fig C

Observation:

1. E is Co-linear with base.
2. Line DE is perpendicular to base.
3. Therefore it will forms rectangle ABE'E.
4. Thus the area of parallelogram = area of rectangle ABE'E
                                                      = breadth X height

 Note:

In some input cases, perpendicular of parallelogram may fall outside the base [E.g. Fig D]. In such cases click on parallelogram to rotate it and follow the same procedure as mentioned above.

Fig D


Result:

Area of parallelogram is the product of its base and height.
 

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