Do you know how to find the area of ​​a triangle?

Do you know how to find the area of ​​a triangle?

I have made you wait excessively to know how the area of ​​a triangle is found. That waiting is good in some aspect. We have learned many important mathematical concepts. So you will find yourself getting more sophisticated in finding out how to find the area of ​​a triangle.

Now take a rectangle. Draw a diagonal connecting its opposite corners. Notice also that this diagonal line divides the rectangle into two equal parts.

Now if we divide the rectangle along the diagonal we get two triangles? Aren't these two triangles equals since the diagonal bisects the rectangle equally?

If you are in doubt, draw a diagonal line on an A4 sheet and cut it along the diagonal and match it lengthwise and widthwise will be equal.

It doesn't have to be A4 paper, legal paper is also fine. Or any rectangular sheet of paper or cardboard is also ok. You can check the above fact by drawing its diagonal and then cutting it along the diagonal.

Now don't you know that a rectangle contains two equal triangles? So we can express the area of ​​a rectangle as the area of ​​two equal triangles. Then the area of ​​the triangle can be stated as half of the area of ​​the rectangle. That is

Area of ​​rectangle = 2 × area of ​​triangle

½ × area of ​​rectangle = area of ​​triangle

Now change what's on the right to the left and what's on the left to the right.

It is true that area of ​​triangle = ½ × area of ​​rectangle.

So the area of ​​the triangle is ½lb square units. right?

As far as the triangle is concerned, l of the rectangle will be taken as the base and b of the rectangle will be taken as the height.

Don't ask what the fuss is all about. Do I need to mention that l and b are variables in the formula for the area of ​​a rectangle? So we can define variables and change them. This is what we saw earlier in the definition of variables.

Accordingly let us take l of the rectangle as b to represent the base of the triangle and b of the rectangle as h to represent the height of the triangle. Now see how the formula for the area of ​​a triangle works out.

Area of ​​triangle = ½bh square units? This is the formula for the area of ​​a triangle.

Tell us what it would be like if we did on square paper what we did on rectangular paper? You don't need to cut the diagonal triangles and fold them along the diagonal to see if they are equal. Now do you do it?

Then what will be the area of ​​the triangle? Is that half the area of ​​the square? That is ½a² square units.

In this triangle the side of the square is the base and height of the triangle so you can take a as b or h as per the definition of variables. So you can define the area of ​​the triangle as ½b² square units or ½h² square units however you want. Because in this case does not b = h? Our clear knowledge of the variables helps us arrive at this conclusion. I hope you understand by now that that's why we're going to go into some detail in some places.

Now you have a question? That is, you have put a right triangle and shown that the area of ​​the triangle is half the area of ​​the rectangle. Is this suitable for acute and obtuse triangles? I have already told you that of course it will be. Don't you need proof though? We will see it tomorrow.

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