Before looking at the area of a triangle…
I said yesterday that
the area of a triangle is half the area of a rectangle. I was also asking you to think
about it. You will also think.
Before that we need to
see a few things. There are four so-called fundamental geometrical forms in
mathematics. They are, 1. Square, 2. Rectangle, 3. Triangle, 4. Circle.
A square is a shape
with all four sides equal. Do fifty fifty biscuits come to mind when you think
of square? Also, if it is a square, then the diagonals must be equal. If we ask
whether there is a shape whose diagonals are not equal, all four sides are
equal. Its name is rhombus. Don't be afraid that such a form suddenly emerges
after saying that there are four basic geometrical forms. We are going to see
about it very simply later.
A rectangle is a figure
whose length and breadth are equal. When you think of rectangles, do you think
of Milk Bikis biscuits? Also, if the rectangle is a rectangle, the diagonals
must also be equal. Otherwise it will become parallelogram. Let's call it a
slanted rectangle. Don't be afraid of new shape again. Let's see about this
very simply later.
If you ask what you
mean by this, when you say area, you have to consider the diagonals just as you
have to consider the product of adjacent sides. We need to talk about it now
because the diagonals will play an important role in calculating area in later
forms. So now we have to be careful about area and diagonal as well as product
of adjacent sides.
That's right. You have
no confusion about the diagonal. Don't you know that a diagonal is the line
that joins the corners of a shape?
Now come to the area of
the triangle, you say?
Before that, let's see a little bit about the circle. Does circle make you
think of Mary Biscuits? Let that be enough. If I talk more than this, you will
not adjust me. Let's learn more in detail when we look at the circle. I don't
stop your interest in finding the area of the triangle any longer.
Would you believe that
triangle is the biggest subject in mathematics? Trigonometry is a separate
paper in the degree course. You wonder if there is a separate sheet for the
samosa-like triangle.
A triangle is a figure
enclosed by three sides, but there are many types. All three sides of a
triangle may be equal if the sides are taken. Otherwise, only two sides can be
equal. Otherwise, all three sides may be unequal. Right, so there are three
types of opportunities?
Thus, when viewed in
terms of sides, if all three sides are equal, then the triangle is called an
equilateral triangle. If only two sides are equal, it is called an isosceles
triangle. If all three sides are unequal, it is called a scalene triangle.
These three types of
triangles can be acute triangles, right-angled triangles or oblong-angled
triangles based on the angles. What do you call the next classification? Is
that it? If a triangle has three sides, must it have three angles? It is a
classification based on how those three angles are formed.
Think for yourself. A
triangle means that all three angles can be acute. Or it can be two acute
angles and an obtuse angle. All three angles cannot be obtuse because there is
a rule in mathematics that the sum of the three angles of a triangle must come
to 1800. We will see if this rule is correct later. So two obtuse angles
are not even possible in a triangle. Only one obtuse angle is possible in
triangle.
Or alternatively a
triangle may have one right angle and two acute angles. I need not explain why
it is not possible for two right angles to form a triangle. Because the sum of
the angles of a triangle must be within 1800. If there are two right
angles then the sum of the two right angles will be 1800. There will
be no chance of a third angle in a triangle. A triangle is possible only if
there are three angles. Is it clear now?
Just as we classified
triangles based on sides, we can now classify triangles based on angles.
A triangle is an acute
triangle if all three angles are acute angles. If any angle is obtuse, then it
is an obtuse triangle because an angle itself can be obtuse. Similarly, if any
angle is a right angle, then it is a right triangle.
Equilateral triangles
are acute triangles. Isosceles triangles can be acute triangles or right
triangles or obtuse triangles. Scalene triangles can also be right-angled
triangles or acute triangles or obtuse triangles.
So no matter how you
draw or construct a triangle, it will either be an acute triangle, or a right
triangle or an obtuse triangle. You cannot draw or construct any other type of
triangle.
So don't be afraid that
there are three types of area formulas for these three types of triangles. The
formula for area is the same for all three types of triangles.
We are those who insist
on testing any mathematical truth. So we have to see if the concept of half of
the area of the rectangle that we have said as the area of the triangle is
applicable to these three types of triangles.
Do you now understand
why we keep putting off the formula for finding the area of a triangle? So today we
are not going to look at the formula for the area of a triangle. We will see
tomorrow. I know very well that you must be angry with me now.
If we look at the
formula with a clear understanding it will never forget you. That's why after
so much understanding, tomorrow we will definitely look at the area of the triangle.
*****
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