Area of ​​parallelogram and area of ​​obtuse triangle

Area of ​​parallelogram and area of ​​obtuse triangle

An obtuse triangle cannot be constructed in such a way that the entire base of a rectangular sheet is the base of the triangle.

Only acute triangles and right triangles can be constructed so that the entire base of the paper is the base of the triangle. What do we do now?

Let's do a small redesign on the paper we take (A4 paper or Legal Size paper or Rectangular paper or Rectangular card).

Let's draw a line on the left side of the rectangular paper and cut the paper along that line and join it to the right side of the paper.

 

Now the sheet will look like this.

 

The shape of the paper we have now is called the parallelogram. There is one thing we need to notice. The shape of the rectangle has changed parallelogram, but there is no change in the size of the rectangle i.e. the area?

We have added what was cut in this area to that area! How else would the area change? So here the area of ​​the rectangle is the same as the area of ​​the parallelogram. The shape has changed but the area enclosed by the shape is the same size as when it is rectangular and the same size when it is parallelogram.

Before we find the area of ​​an obtuse triangle, we have found the formula for the area of ​​a parallelogram.

Here,

It is true that area of ​​rectangle = area of ​​parallelogram.

When taken as a parallelogram, the length of the rectangle is taken as its base i.e. b. Similarly the width of the rectangle is taken as the height of the parallelogram i.e. h. so,

The area of ​​a rectangle is lb square units while the area of ​​a parallelogram is bh square units. So l becomes b and b becomes h. As you know we can define variables and change them.

Can we say area of ​​rectangle = lb = bh = area of ​​parallelogram?

Here's another thing you should keep in mind.

Do not multiply successive side measures when finding the area of ​​a parallelogram just as you multiply successive side measures when finding the area of ​​a rectangle. Because here we take base and height for area. i.e., You have to remember that the bottom side of the parallelogram and not the adjacent slanted side of the parallelogram.

You mean right? I hear you ask that we have not yet arrived at the formula for the area of ​​an obtuse triangle.

Let's start working on it. That is why we are doing so much work.

Now let's take the rectangle that we have converted parallelogram.

Draw and cut a diagonal as shown in the figure to connect its corners.

 

Fit the cut area. Turn the top triangle upside down and match it left and right. Can two equal obtuse triangles be found? These two obtuse triangles form a parallelogram?

Then the area of ​​the obtuse triangle is half of the area of ​​the parallelogram. That is ½bh square units. Here the base of the parallelogram is the base of the obtuse triangle and the height of the parallelogram is the height of the obtuse triangle so without changing the variables for the formula we get the area of ​​the triangle as ½bh square units.

But I do not fail to hear that you ask whether the area of ​​a triangle is half the area of ​​a rectangle.

The parallelogram we have constructed is a re-shape cut from the rectangle without changing the area. Seeing that the area of ​​a parallelogram and the area of ​​a rectangle are equal, we set out to find the area of ​​an obtuse triangle.

So are we right? That means the area of ​​a triangle is half of the area of ​​a rectangle.

So far we have taken three types of triangles namely acute triangle, right triangle and obtuse triangle and proved that its area is half of the area of ​​a rectangle.

For this we have come across a long travel path but interesting path! And in trying to find the area of ​​an obtuse triangle, we have also found the formula for the area of ​​the parallelogram, and we have hit two mangoes with one stone.

Tell us what we should see next! Yes you got it right? We will see it tomorrow.

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