Do you know find the area of ​​the rhombus?

Do you know find the area of ​​the rhombus?

Although a rhombus has a structure similar to a square, there is a difference between a square and a rhombus.

Although the four sides of a rhombus are equal as to the four sides of a square, the diagonals of a rhombus are not equal to as the diagonals of a square. This difference is what differentiates a rhombus from a square.

Students are asked to remember the shape of a diamond when they are asked to draw a model picture of a rhombus to make it easier to remember.

Let us first look at the shape of a rhombus in which all four sides are equal and the diagonals are not equal.

This is the rhombus. We must not forget that if its diagonals are equal, it becomes a square.

Don't forget that we said that diagonals help us a lot when finding at area.

Now let's draw diagonals to this rhombus. First let's draw the horizontal diagonal.

What do you think of when you see this horizontal diagonal? Doesn't this diagonal divide the rhombus into two triangles?  You understand now?

That's right, if you find the sum of the areas of these two triangles in the same way you found the area of ​​a quadrilateral, by now you will have found the formula for the area of ​​a rhombus?

Does this horizontal diagonal form a triangle above and a triangle below and is the base of both triangles i.e. b?

Now all we need are the heights of the triangles? For that we just need to draw the vertical diagonal of the rhombus. How do you draw that? Like this, look at the picture.

Now you can see that this vertical diagonal also sets the diagonal as a set of two triangles, left and right.

Next you need to know a mathematical fact about the diagonals of a rhombus.

Cut out the rhombus we have drawn on the same paper and fold it along the horizontal diagonal. Now you will understand a truth. It means that the vertical diagonal is bisected by the horizontal diagonal. Similarly if we fold through the vertical diagonal we can see that it bisects the horizontal diagonal. What is right?

And another fact that can be seen here is that the upper and lower triangles are equal when folded along the horizontal diagonal. Similarly, when folded along the vertical diagonal, the right and left triangles are also seen to be equal.

Since we have drawn two diagonals for the rhombus, let's denote the horizontal diagonal by the variable d₁ and the vertical diagonal by the variable d₂ to distinguish between the two.

When we look through the horizontal diagonal we get a triangle at the top and a triangle at the bottom, don't we? The sum of these two triangles is the area of ​​the rhombus. Also, aren't these two triangles equal? So if we find the area of ​​any one triangle and multiply it by two, we can get the area of ​​the rhombus, right?

Do we just find the area of ​​the triangle above and multiply it by two?

The base b of the triangle above is d₁ we are concerned here? Also, the height h of the triangle is half of the vertical diagonal we are concerned here? Since it's the vertical diagonal of 90⁰ and it's bisected by the horizontal diagonal, isn't the height here d₂/2?

You can also see this in the image below.

So the area of ​​the triangle is ½bh square units so here ½d₁×(d₂/2) square units is correct?

Now since the area of ​​the rhombus is 2 × the area of ​​the triangle,

Area of ​​rhombus = 2 × ½d₁×(d₂/2) square units. So if we multiply the 2 above by the 2 below d₂, we get ½d₁d₂ square units? It is the formula for the area of ​​a rhombus? What do you understand?

Next we need to find the formula for the area of ​​a trapazium. Will we see it tomorrow?

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