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Let's do this question, find the area enclosed by this equation over here.

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Now remember, Gmod means you take the positive value.

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For example, more of minus two gives you two.

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More of two also gives you two to more means.

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Always take the positive, irrespective of the given number being negative or positive.

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All right.

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Now let's proceed over here.

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You have given your given this equation that is four more X plus five more weigh less than equal to

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twenty.

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Right now, this over here represents four straight lines.

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Now, let's see how that is.

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Let me mention it over here.

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All right, now let me right the four straight lines that are represented by this equation, how do

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you get them?

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You either take excess, positive or negative can be positive or negative and y also can be positive

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or negative.

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That's two ways.

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And this is also two ways.

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So two in the two, that's how you get four straight lines.

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Let's write them over here.

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Or X plus five is equal to 20 over here.

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Both of them are taken as positive or into minus X, plus five is equal to twenty.

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We we this one is negative and this is positive.

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And then you have four X plus five into minus way.

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This is positive.

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This is negative.

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And over here you have four minus X, plus five minus Y is equal to twenty where both are taken as negative.

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So these four lines are represented by this equation over here.

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Now remember, I'm taking it as equal to to get the border in this equation over here.

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It's mentioned as less than equal to.

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Let's see what the implication is.

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Now, first, let me start with plotting these four equations that we have arrived at.

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All right, so I have my access and I plotted like this now how do we do the plotting?

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It's very simple.

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You just need to find two points to plot a line right now.

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Let's take this line over here.

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Let's clean this up a little bit, OK?

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Now let's take the first one over here.

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Over here, four X plus five is equal to zero is equal to 20.

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So if X is equal to zero, that's zero plus five is equal to 20.

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So Y will be equal to four.

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Right.

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So zero comma four is one of the points of this line over here.

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So let's plot zero comma four.

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That's zero zero.

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And then on the Y axis, you need to go for units.

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That's one, two, three, four.

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To this point over here is zero comma four.

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Right.

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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.

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So five zero is also lying on this line.

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So let's plot that over here.

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One, two, three, four, five.

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So this is five comma zero.

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So I have two points.

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And when I join them, I get this line over here.

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So if this is the first line, that's this line over here.

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All right.

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Let's plot the next one over here.

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If I put X is equal to zero, I get why is equal to four.

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Right.

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That's zero comma for that at this point over here, which we have already plotted.

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And if I put Y is equal to zero, that's minus four.

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X is equal to twenty.

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So X has to be equal to minus five.

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So this point over here is minus five from a zero.

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And when I join them I get this line over here.

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So if this is line two, that's this line over here.

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All right.

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Now let's proceed to the third line.

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I have four X plus five in the minus 20.

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So when X is equal to zero, Y has to be equal to minus four.

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So that's this point over here, which is zero minus four.

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Right.

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And when Y is equal to zero, X is equal to five.

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That's this point over here.

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So this over here is line three.

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This is line three.

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Right.

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And over here, both of them are negative.

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So when X is equal to zero, Y has to be minus four.

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That's this point.

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And when Y is equal to zero, X has to be minus five.

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That's this point.

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I joined them together and I get nine four over here.

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All right.

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Now, over here it is mentioned that it's less than equal to.

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Right.

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So when you plot this line over here, you need to take this line and everything to decide because it

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has to be less than that value.

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Similarly, when you plot this line, you need to take things that are in this direction.

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Right.

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And over here, you need to take things that are in this direction.

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And for this line, you need to take points that are in this direction.

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So you end up getting this shaded region.

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And that is what you need to find out, right?

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It's mentioned find the area enclosed by this equation over here.

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This is the area that you need to find out right now.

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Let me clean this up a little bit so that we proceed.

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We have seen how to plot these lines and find the enclosed area that we are trying to find out geometrically.

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We have represented it on the access all.

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Now, what are these four points?

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Remember, we found them out, right?

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This is five zero zero four minus five zero and zero minus four.

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Now we just need to find this area.

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Now you can see that over here, this right angled triangle as sites or units over here and five units

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over here.

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Right.

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And over here.

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Also, this right angled triangle has four and five units similar to this one also has four units over

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here and five units over here.

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This one also has four units over here and five units over here.

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So you just need to find one area of a triangle and multiply it with four.

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Now, we know area of this triangle is half base in the height.

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That would be half in two or in five.

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Right to the required area.

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That is this area over here would be four times off into four and five.

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And that gives you 40 units square as the area.

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And that is your answer.