Hi friends, in our previous session we have
learned how to find perimeters quadrilaterals. If you havent watched it yet, you can watch
it after this session. Lets move further, Now we will go inside the boundaries and find
the area. We will try to simplify it by using triangles
and I m sure after this we will not only find it simple but also there wont be any need
to learn it by heart. Because logic and common sense are never mugged-up.
Lets proceed, Guys we know that any quadrilateral diagonally
can be divided into two triangles, right?? And area of a triangle is = (base*height)
But some of our friends get confused about the height of the triangles.
For example in this triangle, we say the height is AB but this is not true. The height is
always the perpendicular height not slant, here AB is slanted.
But if the triangle is a right angled triangle in this case only AB is the perpendicular
distance i.e height of the triangle.
Triangles play a very important role in finding and formulating the areas of Quadrilaterals.
Seems strange right?? Something which is rarely seen, lets see how it works!
We will be finding areas all types of quadrilaterals by only using the area of a triangle. So what
do we have to keep in mind?? Area of triangle = (base*height)
Lets again start with our first family the parallelogram family.
There are four members in the parallelogram family.
(1) Parallelogram (2) Rectangle (3) Rhombus (4) Square
We have to follow these three steps:
Divide all of them into two triangles Add the areas of these two triangles
Arrange them and derive the formula
First we will find the areas of parallelogram and rhombus and then we will go for rectangle
and square. When we cut them we get two congruent triangle,
we will find area of triangle and add them up to get the area of parallelogram.
Lets name them as ABCD so here triangle ABC and triangle ADC are congruent if we double
the area of triangle ADC it will give us total area of parallelogram ABCD and procedure will
be same for rhombus. Now you tell me what is the area of triangle
ADC?? For that we need height so lets consider H
is the perpendicular height so area of triangle ADC = (DC*H)
Now double it up so we will get DC*H, where DC is base.
In general we can say area of parallelogram is base*height.
Area of all members of this family can be found by this formula only because every can
be divided into two congruent triangles so area of all member will be (base*height).
The only difference is in rectangle and square we get two congruent right angled triangles
so height is AD or BC only and therefore area of square is calculated as (side*side) = (side)2
because it all sides are equal.
But the core idea behind all is (base*height)
By this we are done with the parallelogram family and I hope you will find it simple
and interesting.
Lets try to find the area of the trapezium family with the same logic on our own.
Follow the first step: Divide all the types of it into two triangles.
now we will find area for both the triangles respectively because these triangles are not
congruent unlike parallelogram.
Second step: Now consider parallel sides of it as bases for respective triangles so that
height will be same for both the triangles because they are drawn in parallel line segments,
ok?
Third step: Add the areas of two triangles
Area of trapezium ABCD = (CD*h) + (AB*h) = *h(AB+CD)
= (addition of parallel lines)*height
Isnt it easy and seems meaningful as well now!!
Can you do it for a kite?? Lets do it together, We can divide a kite into two triangles in
two different ways. Lets see first, what happens if divide it
horizontally, First step that is division is done, now lets
do the next step,
Area
of kite = (BD*h1) + (BD*h2) = (h1+h2)BD
= (first diagonal of kite)*(BD=second diagonal of kite)
Therefore we say that area of kite is (product of the length of the diagonals)
Let�s follow the same steps if we cut a kite vertically and see whether we get the
same formula or not?? This is a home work you, try it I m sure you will get the same
formula.
By now you need not to remember any formula. Just divide them in two triangles and find
the area by using (base*height).
Friends let me tell you an important thing that area of parallelogram can also be found
by using the formula of trapezium.
Now you might be thinking can we find the area of trapezium by using formula of parallelogram.
No, this will not work.
One more thing must have come in your mind that if rhombus and square also belong to
kite family so can we use kites formula to find their area..
If you havent thought it then think it and write your opinion in the comment box as yes
or no.
Friends dont try to simply mug up things without understanding it. Math is not a problem it
is a tool to simply things and makes everything easy and convenient.
Lets see what we learned in todays session. This is it for today, write your queries and
difficulties in the comment box and subscribe to letstute. Keep watching keep learning.
Thank you!