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Students in this video, let's learn how to find the area of a triangle encoded geometry, right.

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If you're given that vertices of the triangle, let's find out how to find the area of the triangle.

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All right.

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Now we will discuss two methods in which you can do this.

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And the best way to learn this is with an example.

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Over here we have three.

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What is given right now?

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Let's plot these points.

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OK, so I have my X and Y axis over here.

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Now, let me plot these three points, right?

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So this is seven nine.

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This is 10.

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Come on, eight.

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And this is zero zero, right?

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That's the origin.

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Now, let me join these three vertices to form a triangle.

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All right, now over here, you can see that if I can strike this Ebbie NBC in this manner, right,

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you get a rectangle over here, right?

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What did I do?

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I took the farthest y coordinate.

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So over here I have nine.

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Over here I have eight.

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So I took nine.

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And I draw a line like this.

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Right.

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This is this this line over here is why is equal to nine.

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Right.

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And over here I take the farthest X coordinate but that's seven over here.

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This is ten over here.

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So that X is equal to ten, I draw a line.

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So this line over here, we see if you extended this line over here is the line X is equal to ten right

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now.

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If you take any point on this line, your X coordinate will be ten.

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Similarly, if you take any point on this line, your Y coordinate will be equal to nine.

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Right.

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So this line over here is the line X is equal to ten.

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And this line over here is the line Y is equal to nine.

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All right, now, both of them intersect at point B over here, which is the point X will return, right.

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And what would be right?

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Why would be nine?

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So the intersection point B over here is then comma nine, right.

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Let me right that over here.

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All right.

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Now, what would be the area of the rectangle ABC or let me make some space over here, the area of

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Rectangle ABC or would be 10 to nine.

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Right.

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Because this distance over here is ten.

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This is 10.

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And this distance over here is nine.

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But we know that area of a rectangle is well into B or side into the other side.

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So you get ten in the nine.

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That's 90 as the area of A, B, C or right at this point over here, seven nine B, B and let ten,

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eight be cute.

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All right.

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Now, over here, if we want to find the area of Triangle or B Cube, we just need to find the area

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of these three triangles.

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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

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of the rectangle.

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Then from the figure, it's clear you get the area of triangle P Q.

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All right, let's take that approach over here first.

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So let's find area of triangle A or B, what would that be.

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That would be half in two nine two seven.

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That's sixty three by two.

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Right.

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Because we know area of a triangle is half base in the height.

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So I take this or as the base in that case AP will be the height.

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Right.

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Because this is the right angle and a B we know is equal to seven.

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Right.

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Because the X coordinate of point B is seven.

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All right.

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Now what would be the area over here?

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That's this area, right?

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This is equal to sixty three by two.

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Now let's proceed.

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What is the area of curacy, the area of Curiosity's half window then into it right over here.

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You take the base as then that's this one over here or C and in that case you see will be the height

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and point you has a Y coordinate of eight, therefore the height is equal to eight.

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Right.

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So the area of curacy is equal to half an inch to eight.

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That's equal to forty.

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And that is this area over here.

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Now let's find the area of triangle P, Q, B, that would be half in the three to one.

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Right, because over here I have the Y coordinate as nine for this line and the Y coordinate of Q is

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eight, so nine minus eight is one.

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So BQ is equal to one.

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And similarly you can find that B, B is all C minus AP or C is equal to ten and AP seven, so then

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minus seven gives you three and hence the area of Triangle P.

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Q is half three and one.

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That's equal to three by two.

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That's this area over here now to find the area of Triangle P or Q, all you need to do is you need

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to subtract these three values from ninety.

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Right.

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So that's ninety minus sixty three by two, minus four T minus three by two and that is equal to seventeen.

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All right.

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So this is the first approach that we discuss where you can find the area of a triangle.

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Now let's discuss one more approach, which is also very quick now to find the area.

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When you are given three vertices, we have given three words as, all right, all you need to do is

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you need to write the words this like this we have x1 wyvern x2 y2 x three, y three and again, x1

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wyvern.

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And you write them like this and you write half over here right now.

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What do you do.

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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

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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

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the difference.

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That is.

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Let's take an example to understand it over here we have these three.

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What is this, do we write them over here in this manner we have zero zero.

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That's this Vertex seven nine.

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That's this one then eight and again, zero zero.

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So anyone can be the first one which has to be repeated over here.

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All right.

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Now, zero into nine plus seven into eight plus ten into zero.

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Right.

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That's equal to fifty six.

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Right.

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So you have a half over here.

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So that's half in two.

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Fifty six minus.

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Then you take this, that's seven to zero Palestinian to nine zero in the eight.

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That's equal to ninety.

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So you take the difference.

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So the area would be half into fifty six minus ninety and you always need to take the areas positive,

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like fifty six minus ninety gives you a negative value, but the area similar to the distance has to

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be taken as positive.

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That would be the area of this triangle.

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How much is fifty six.

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Minus ninety.

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That's minus thirty four.

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So you take the positive value.

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So the area is equal to thirty four.

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Divided by two.

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That's equal to seventeen.

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That's the same value that we got over here.