Mathematical facts about area

Mathematical facts about area

The product of a square in a table i.e.,

1 × 1 = 1

2 × 2 = 4

3 × 3 = 9

4 × 4 = 16

… … … all represent the area of ​​the square. All the rest represent the area of ​​the rectangle. This is what we saw yesterday. All the rest means everything that is not included in the above. For example

2 × 3 = 6 is the area of ​​a rectangle that is two units long and three units wide. Check out the picture below.

Is there a unit of length 3? Is there 2 units of width? Multiply both and get 6? There are only square grids inside. I think this one example is enough.

I understand what you're asking to say something else though. Because it is better to think twice before accepting something.

Now take 5 × 4 = 20. Now we have taken a rectangle of length 5 units and width 4 units. You must have seen this picture in your mind's eye by now. Here is the picture in your mind's eye

 

Look at this 5 by 4 rectangle. The square grids inside are only 20 in number.

So what we found is correct. The entire table is the area of ​​squares and the area of ​​rectangles. It will now be ingrained in your memory that you are telling the area of ​​a square or the area of ​​a rectangle when you say each step of the table.

Now you must have thought that the area of ​​a triangle and the area of ​​a circle are not possible as mentioned above. Since we cannot count the complete square grids as in the form of square, rectangle in the triangle and circle, they will be in a certain proportion of the potential multiplier. What is that specific ratio you ask?

Before that, let's look at a few more things. Are there any other things? You are asking if it is not done yet.

Now we are going to see the mathematical facts contained in it. Now we need to find the algebraic expression for the area of ​​the rectangle just as we saw the algebraic expression for the area of ​​the square a × a i.e., a²?

Tell yourself, how can you form an algebraic expression for the area of ​​a rectangle? Since we are multiplying two different numbers, you are asking whether x × y means xy. Very well.

But the variable for this i.e. you take x as l and y as b will be taken to match the rectangle. They are taken as l stands for the first letter of the word length and b stands for the first letter of the word breadh. Since this is a case we will also take the algebraic expression for the area of ​​the rectangle as lb.

That is not possible, there is nothing wrong with that if I just mention xy. Whenever you do calculations related to the area of ​​a rectangle, you must remember that x represents the length of the rectangle and y represents the width of the rectangle. If you write lb it goes without saying that you have taken the length as l and the width as b. That's the point.

Now we must deduce an important mathematical fact from what we have seen so far. Only when we find it, we can move on to triangle, circle and its area and circumference.

Whether it is the area of ​​a square or a rectangle, we multiply the adjacent sides to find the area. Oh yes, you say?

Yes, the same. If we take the square we multiply the two adjacent sides. We then multiply the length and width of the next two sides to fit the rectangle. By multiplying like that, we can find out how many square grids will be inside.

No matter whether it is a square or a rectangle, just multiply the adjacent sides to find its area. Its area will be found. This is the mathematical truth we know about it.

Why do we multiply the adjacent sides like this because square, rectangle, triangle and circle are all two-dimensional shapes. So just multiply its adjacent two sides which are two dimensions.

So if three-dimensional figures mean that the third dimension is multiplied by the adjacent two sides to its volume, then you have got the right idea.

Yes, the third dimension of three-dimensional shapes is height. So to find the volume of any three-dimensional shape, just multiply the height with the adjacent side.

See how we progress from one mathematical fact to subsequent mathematical facts. Based on this, can you give the formula for the volume of a cube?

How? You are asking side × side × height. That's right. But cubic Since all side measures are equal, the side measure which is the height is also the side. So its volume is side × side × side. i.e. a × a × a i.e. a³

Similarly, what you are asking is that a cuboid is length × width × height. Correct l × b × h. i.e., lbh. Let's count cubes in volume just like we counted square grids in area. So when we say a³ we have to include a³ cubic unit and when we say lbh we have to include lbh cubic unit. The unit we take is cm. If a³ cubic cm. i.e. Also lbh cubic cm. It should also be mentioned. What is right?

The mathematical truth we have seen applies in any form. So always keep in mind the mathematical fact that the area is multiplied by its adjacent sides. Have I said too much today? I hope it was not difficult for you. Let's reduce it a bit tomorrow.

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