In this video, let's learn how to find the area of a parallelogram.
But over here I have a program and we know opposite sides are equal and parallel in a program to let
this side be a this is also a this is me and this is B, and these two sides are parallel and these
two sides are parallel.
Now from this vertex.
Let me construct an altitude to the opposite side.
All right.
Now, let me cut out this triangle over here and move it down.
And I fix it over here, I fix it to this place over here, so that would look like this.
Now, over here, you can see that it has changed to a rectangle, right?
So this is the shape that we started with.
And over here, the length was a right.
So therefore, this length also is equal to it right now over here, because this is a this also will
be equal to it.
Right.
Why is that so?
Because it's given that this much is it.
All we did was we cut this out and placed it over here.
Therefore, the length of the side does not change.
So this is a this is it.
And let this be it.
This is the altitude that we dropped from here to here.
So let this be it.
Now we have got here a rectangle and the area of a rectangle is equal to side into the other side.
So length in breadth.
In this case, the area of this figure over here is equal to eat into it.
Therefore, we have got that the area of a program is equal to the base into the height.
Right over here is the base.
And it's over, here is the height.
Therefore, area of a program is equal to base in height.
Now, remember, the height is the perpendicular drop on that side from the opposite vertex, or in
this case, we have taken this as the base.
The opposite vertex is over here and we drop it perpendicular to this side.
We could have dropped it from here.
Also, this is also an opposite vertex to this site.
So you will get the same height if you have dropped it from here.
So let's quickly summarize.
We have seen that the area of a program is equal to base in height.
Now, let's have a look over here again now from this vertex, I drop each one.
So in that case, the area of this program is equal to a into each one because it is taken as the base.
Each one is the height.
Now, if I were to take B as the base, let me drop A perpendicular from the opposite vertex to this
side.
So let this be its two, then you can say that the area is equal to be in two x2 and these two are equal.
You will get the same value in this case and in this case.
So to find the area of a program, all you need to know is the base and the corresponding height, right?
If you know this as a and if you know this as it's to, you cannot multiply them.
Right.
You need the corresponding height.
You need to multiply avin each one or be with two to get the area of a program.
Let's see one more interesting concept.
We have a Bananagrams over here, the site is five centimetre and eight centimeter.
Now let's have another parallelogram with the same size.
Well, this is all the five centimetre an eight centimeter window opposite sides in a paragraph about
equal.
Right.
But this is also a five centimeter.
This is also eight centimeters similarly over here.
So this is eight centimeter and this is five centimeters.
So you will see that these two parallelograms have the same perimeter.
But you can see that this angle is not equal to this angle.
These two angles are different.
Right.
That's why over here, it's given that the altitude from the opposite side of this side is two centimeter
in length.
And over here, they already do this three centimeters.
So you will see that though the perimeter is the same, these two parallelograms have different areas.
So remember, just because two parallelograms have the same perimeter or even the same length of the
sides, it does not mean that they will have the same area.
What is the area over here?
It will be two in to eat, right.
That 16 centimeter square.
What is the area over here?
It will be three to eight.
That's twenty four centimeter square.