Let's do this question, find the area enclosed by this equation over here.
Now remember, Gmod means you take the positive value.
For example, more of minus two gives you two.
More of two also gives you two to more means.
Always take the positive, irrespective of the given number being negative or positive.
All right.
Now let's proceed over here.
You have given your given this equation that is four more X plus five more weigh less than equal to
twenty.
Right now, this over here represents four straight lines.
Now, let's see how that is.
Let me mention it over here.
All right, now let me right the four straight lines that are represented by this equation, how do
you get them?
You either take excess, positive or negative can be positive or negative and y also can be positive
or negative.
That's two ways.
And this is also two ways.
So two in the two, that's how you get four straight lines.
Let's write them over here.
Or X plus five is equal to 20 over here.
Both of them are taken as positive or into minus X, plus five is equal to twenty.
We we this one is negative and this is positive.
And then you have four X plus five into minus way.
This is positive.
This is negative.
And over here you have four minus X, plus five minus Y is equal to twenty where both are taken as negative.
So these four lines are represented by this equation over here.
Now remember, I'm taking it as equal to to get the border in this equation over here.
It's mentioned as less than equal to.
Let's see what the implication is.
Now, first, let me start with plotting these four equations that we have arrived at.
All right, so I have my access and I plotted like this now how do we do the plotting?
It's very simple.
You just need to find two points to plot a line right now.
Let's take this line over here.
Let's clean this up a little bit, OK?
Now let's take the first one over here.
Over here, four X plus five is equal to zero is equal to 20.
So if X is equal to zero, that's zero plus five is equal to 20.
So Y will be equal to four.
Right.
So zero comma four is one of the points of this line over here.
So let's plot zero comma four.
That's zero zero.
And then on the Y axis, you need to go for units.
That's one, two, three, four.
To this point over here is zero comma four.
Right.
OK, now if I put why as zero, that's four X plus zero is equal to 20, so X is equal to five, right.
So five zero is also lying on this line.
So let's plot that over here.
One, two, three, four, five.
So this is five comma zero.
So I have two points.
And when I join them, I get this line over here.
So if this is the first line, that's this line over here.
All right.
Let's plot the next one over here.
If I put X is equal to zero, I get why is equal to four.
Right.
That's zero comma for that at this point over here, which we have already plotted.
And if I put Y is equal to zero, that's minus four.
X is equal to twenty.
So X has to be equal to minus five.
So this point over here is minus five from a zero.
And when I join them I get this line over here.
So if this is line two, that's this line over here.
All right.
Now let's proceed to the third line.
I have four X plus five in the minus 20.
So when X is equal to zero, Y has to be equal to minus four.
So that's this point over here, which is zero minus four.
Right.
And when Y is equal to zero, X is equal to five.
That's this point over here.
So this over here is line three.
This is line three.
Right.
And over here, both of them are negative.
So when X is equal to zero, Y has to be minus four.
That's this point.
And when Y is equal to zero, X has to be minus five.
That's this point.
I joined them together and I get nine four over here.
All right.
Now, over here it is mentioned that it's less than equal to.
Right.
So when you plot this line over here, you need to take this line and everything to decide because it
has to be less than that value.
Similarly, when you plot this line, you need to take things that are in this direction.
Right.
And over here, you need to take things that are in this direction.
And for this line, you need to take points that are in this direction.
So you end up getting this shaded region.
And that is what you need to find out, right?
It's mentioned find the area enclosed by this equation over here.
This is the area that you need to find out right now.
Let me clean this up a little bit so that we proceed.
We have seen how to plot these lines and find the enclosed area that we are trying to find out geometrically.
We have represented it on the access all.
Now, what are these four points?
Remember, we found them out, right?
This is five zero zero four minus five zero and zero minus four.
Now we just need to find this area.
Now you can see that over here, this right angled triangle as sites or units over here and five units
over here.
Right.
And over here.
Also, this right angled triangle has four and five units similar to this one also has four units over
here and five units over here.
This one also has four units over here and five units over here.
So you just need to find one area of a triangle and multiply it with four.
Now, we know area of this triangle is half base in the height.
That would be half in two or in five.
Right to the required area.
That is this area over here would be four times off into four and five.
And that gives you 40 units square as the area.
And that is your answer.