A Nice geometry maths question| Find the area of the shaded portion

This is an interesting math question. It's under Geometry. We are told that the area of this square is not drawn to scale. The area of this section is 15. The area of this portion is 6. The area of this section is 14. So the question is, what is the area of this section? Now let's call this face, this particular place, the eye. Now this is eye, eye. This is eye, eye, eye. So we are looking for the area of IV. Remember that this is a rectangle. Now, if this is a rectangle, note that this is not a square. This is a rectangle, this is a rectangle, this is also a rectangle. Now, if we say let this place be equal to A. If from here to here is equal to A, then certainly from here to here will also be equal to A. If we say from here to here, and we say let this be B, then certainly from here to here will also be B. Also, if we say let there be C, then certainly there is also C here. If we call this place D, then this place is certainly also D. Now where am I heading? I would like you to take your time, calm down, and see how we are going to find the value of this rectangle IV. First of all, to find the area of a rectangle, the area of a rectangle is equal to length multiplied by breadth or width. Let's use width. Length times width. That is the area of a rectangle. Now, if we decide to consider rectangle I. Now for I, for the first rectangle which is for I, the area is going to be equal to length times width, which is equal to What is the length? The length is C. So we have C and the width is A. We have A. So from there, this implies that AC is equal to, we already stated that the area is 15. So AC is 15. Also, let's check for I I. So for I, which is this one, the area, let's call this equation 1 to start with. So for me, the area is going to be length times breadth. Now the length is C and the breadth or the width is B. So it's going to be C B or B C. This implies that B C or C B equals the area, which is already 6. Now let's call this equation 2. Now for I, I, I, that is for the third section, for this place. The area is equal to, remember, the area is length times width. So it's going to be D times B, which is the same thing as B times D. So this implies that BD equals 14, since the area is already 14. Now let's call this equation (3). So we have equation 1 as AC equals 15. Equation 2 states that B times C equals 6. Equation 3 as BD is equal to 14. Now let's try to get this. So for 4, which is IV. We can see that the area is equal to, now the length is D. From here to here is D multiplied by the breadth, which is A. So it means that AD is equal to what we are looking for. Let's call what we are looking for X. So let's call this place X, the area we are looking for. And this is equation 4. Now allow me to write down all these equations together so that we can solve them. Now the first one says AC is equal to 15. So let's just write it. Equation 1 states that AC is, I don't know if you can see that there. A C is equal to 15. This is equation 1. Now equation 2 states that BC equals 6. This is equation 2. Now equation 3 states that BD equals 14. This is equation 3. And last but not least, equation 4 states that AD is equal to X. A D is equal to X. This is equation 4. Now I want us to watch this. If we say equation 1 multiplied by equation 3. Multiplying equation 1 by equation 3 will result in A C multiplied by B D. So we have A times C multiplied by B times D equals 15 multiplied by 14. Now, A times C multiplied by B times D is the same as A times B times C times D. So we have A times B times C times D equal to 15 multiplied by 14. Now let's call this equation (5). Let's leave it there. Now, from here, if we say equation 2 multiplied by equation 4. So multiply equation 2 by equation 4. We are going to have B times C multiplied by A times D equal to 6 multiplied by X. Now what we have here is A B C D equals 6 X. Let's call this equation (6). If we call this equation 6, can you see the similarity between equation 5 and equation 6? This is what they have in common. Since ABCD is equal to 15 multiplied by 14 according to equation 5. And A B C D is also equal to 6 X according to equation 6. It simply means that 15 multiplied by 14 equals 6 times X. So we are going to write that 15 multiplied by 14 is equal to 6X. 15 multiplied by 14 is equal to 6X. If we compare equation 5 and equation 6. So look at what we have now. We divide both sides of this equation by 6 to obtain X. So we divide this by 6 and divide that by 6. Now 6 we divide by 6 and we have X is equal to... Now here, 3 we divide this to give us 2. We divide this to get 5. 2 divided by itself gives us 1. Divide 14 to give us 7. So X will give us 5 times 7, which will result in 35 square meters. That is the area of X. If this is the first time you have seen us, please click the subscription button. 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