Area of parallelogram

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

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:

- Create a parallelogram ABCD with length L and breadth B.[Fig C]
- Draw perpendicular from A to DC meeting at point E.
- Click on "Set Square" in Tools to use it.
- Drag and place Set Square such that point A and line DC is perpendicular.

- Click on ▲ AED to separate it from parallelogram.
- Drag ▲ AED and place it such a way that AD is overlapped with BC.
- Please see the observation

**Fig C**

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.