Students in this video, let's learn how to find the area of a triangle encoded geometry, right.
If you're given that vertices of the triangle, let's find out how to find the area of the triangle.
All right.
Now we will discuss two methods in which you can do this.
And the best way to learn this is with an example.
Over here we have three.
What is given right now?
Let's plot these points.
OK, so I have my X and Y axis over here.
Now, let me plot these three points, right?
So this is seven nine.
This is 10.
Come on, eight.
And this is zero zero, right?
That's the origin.
Now, let me join these three vertices to form a triangle.
All right, now over here, you can see that if I can strike this Ebbie NBC in this manner, right,
you get a rectangle over here, right?
What did I do?
I took the farthest y coordinate.
So over here I have nine.
Over here I have eight.
So I took nine.
And I draw a line like this.
Right.
This is this this line over here is why is equal to nine.
Right.
And over here I take the farthest X coordinate but that's seven over here.
This is ten over here.
So that X is equal to ten, I draw a line.
So this line over here, we see if you extended this line over here is the line X is equal to ten right
now.
If you take any point on this line, your X coordinate will be ten.
Similarly, if you take any point on this line, your Y coordinate will be equal to nine.
Right.
So this line over here is the line X is equal to ten.
And this line over here is the line Y is equal to nine.
All right, now, both of them intersect at point B over here, which is the point X will return, right.
And what would be right?
Why would be nine?
So the intersection point B over here is then comma nine, right.
Let me right that over here.
All right.
Now, what would be the area of the rectangle ABC or let me make some space over here, the area of
Rectangle ABC or would be 10 to nine.
Right.
Because this distance over here is ten.
This is 10.
And this distance over here is nine.
But we know that area of a rectangle is well into B or side into the other side.
So you get ten in the nine.
That's 90 as the area of A, B, C or right at this point over here, seven nine B, B and let ten,
eight be cute.
All right.
Now, over here, if we want to find the area of Triangle or B Cube, we just need to find the area
of these three triangles.
That is E, B or P, Q, B and Q or C, and then if we subtract those areas from 90, that is the area
of the rectangle.
Then from the figure, it's clear you get the area of triangle P Q.
All right, let's take that approach over here first.
So let's find area of triangle A or B, what would that be.
That would be half in two nine two seven.
That's sixty three by two.
Right.
Because we know area of a triangle is half base in the height.
So I take this or as the base in that case AP will be the height.
Right.
Because this is the right angle and a B we know is equal to seven.
Right.
Because the X coordinate of point B is seven.
All right.
Now what would be the area over here?
That's this area, right?
This is equal to sixty three by two.
Now let's proceed.
What is the area of curacy, the area of Curiosity's half window then into it right over here.
You take the base as then that's this one over here or C and in that case you see will be the height
and point you has a Y coordinate of eight, therefore the height is equal to eight.
Right.
So the area of curacy is equal to half an inch to eight.
That's equal to forty.
And that is this area over here.
Now let's find the area of triangle P, Q, B, that would be half in the three to one.
Right, because over here I have the Y coordinate as nine for this line and the Y coordinate of Q is
eight, so nine minus eight is one.
So BQ is equal to one.
And similarly you can find that B, B is all C minus AP or C is equal to ten and AP seven, so then
minus seven gives you three and hence the area of Triangle P.
Q is half three and one.
That's equal to three by two.
That's this area over here now to find the area of Triangle P or Q, all you need to do is you need
to subtract these three values from ninety.
Right.
So that's ninety minus sixty three by two, minus four T minus three by two and that is equal to seventeen.
All right.
So this is the first approach that we discuss where you can find the area of a triangle.
Now let's discuss one more approach, which is also very quick now to find the area.
When you are given three vertices, we have given three words as, all right, all you need to do is
you need to write the words this like this we have x1 wyvern x2 y2 x three, y three and again, x1
wyvern.
And you write them like this and you write half over here right now.
What do you do.
You multiply X one with Y two x2 with Y three and X three with Y one and you add that up and then you
multiply x2 with Y one x three with Y two and X one with Y three and you add that up and then you take
the difference.
That is.
Let's take an example to understand it over here we have these three.
What is this, do we write them over here in this manner we have zero zero.
That's this Vertex seven nine.
That's this one then eight and again, zero zero.
So anyone can be the first one which has to be repeated over here.
All right.
Now, zero into nine plus seven into eight plus ten into zero.
Right.
That's equal to fifty six.
Right.
So you have a half over here.
So that's half in two.
Fifty six minus.
Then you take this, that's seven to zero Palestinian to nine zero in the eight.
That's equal to ninety.
So you take the difference.
So the area would be half into fifty six minus ninety and you always need to take the areas positive,
like fifty six minus ninety gives you a negative value, but the area similar to the distance has to
be taken as positive.
That would be the area of this triangle.
How much is fifty six.
Minus ninety.
That's minus thirty four.
So you take the positive value.
So the area is equal to thirty four.
Divided by two.
That's equal to seventeen.
That's the same value that we got over here.