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Triangle | Area and Perimeter of a Triangle

Types Of Triangle:
acute triangle:
An ACUTE (all angles are acute) triangle contains three acute angles (each angle of an acute triangle is less than 90 degrees).sum of the angles of a triangle is always 180 degrees.An acute triangle may be isosceles,scalene or equilateral.

obtuse triangle:
Obtuse triangles have one angle that is greater than 90° degrees.(Obtuse triangles have one obtuse angle).sum of the angles of a triangle is always 180 degrees.An obtuse triangle may be scalene or isosceles.

right triangle:
The right triangle has one 90 degree angle and two acute (< 90 degree) angles.sum of the angles of a triangle is always 180 degrees.A right triangle may be scalene or isosceles.

Equilateral Triangle (समभुज त्रिकोण):
Equilateral Triangle is a Triangle in which all three sides are equal in lenght,equilateral triangle are also equiangular(angles are equal to each other, which is possible if all angles is equal to 60 degree).Now we can define equilateral triangle as "a triangle in which Angles and lenght of three side is equal", given picture/image of equilateral triangle below

Area of an equilateral triangle:
s is the length of one side of the triangle, and 
Area
 of equilateral triangle=
3
4
s
2

Height/altitude of equilateral triangle Formula=s/2 x √3
Perimeter of equilateral triangle Formula=3s

Types of equilateral triangle
acute equilateral triangle:
An ACUTE equilateral(all angles are acute) triangle contains three acute angles (each angle of an acute triangle is less than 90 degrees).sum of the angles of a triangle is always 180 degrees. An acute triangle may be isosceles, equilateral, or scalene.

equiangular triangle:
In an equiangular triangle, all the angles are equal—each angle equal to 60 degrees. An equiangular triangle is a kind of acute triangle, and equiangular triangle is always equilateral.

Is it possible to have a equilateral right triangle?
No(because in right triangle all angles are not equal)
Is it possible to have a equilateral obtuse triangle?
No(because in obtuse triangle all angles are not equal)


Definition of An isosceles triangle(समद्विबाहु त्रिकोण):
A Triangle with two equal side is an Isosceles Triangle(if two side of triangle equal in length then two angles of triangle also equal), So now Defintion is like "A Triangle with two equal side and Two equal Angles" is an isosceles triangl.lenght a=b and angle α is equal(see in below picture/image)

isosceles triangle theorem
if angles, then sides: If two angles of a triangle are congruent, then the sides opposite those angles are congruent.
If sides, then angles: If two sides of a triangle are congruent, then the angles opposite those sides are congruent.

Area and Perimeter of isosceles Triangle
perimeter of isosceles triangle=2a+b
Area of isosceles Triangle=1/2*b*h
here h=height of isosceles Triangle,b=base of isosceles Triangle



Types Of isosceles Triangles
acute isosceles triangle:
An ACUTE isosceles(all angles are acute) triangle contains three acute angles (each angle of an acute triangle is less than 90 degrees).sum of the angles of a triangle is always 180 degrees. An acute triangle may be isosceles, equilateral, or scalene.

obtuse isosceles triangle:
Obtuse isosceles triangles have one angle that is greater than 90° degrees.(Obtuse triangles have one obtuse angle).sum of the angles of a triangle is always 180 degrees.An obtuse triangle may be scalene or isosceles.

right isosceles triangle:
The right isosceles triangle has one 90 degree angle and two acute (< 90 degree) angles.sum of the angles of a triangle is always 180 degrees.A right triangle may be scalene or isosceles.



what is a scalene triangle(विषमभुज त्रिभुज):
Simple definition of scalene triangle is: A Triangle in which No equal angles and no equal sides

As you can see in above triangle all sides with different lengths(AB,BC,CA not equal in lenghts) and Angles also not equal(68,71,41), so a triangle with no equal sides and Angles called scalene triangle(see above image/picture of scalene triangle).sum of the angles of a triangle is always 180 degrees.

Area of a scalene triangle:
s = (a + b + c) / 2
area of scalene triangle = sqrt(s * (s - a) * (s - b) * (s - c))

Types Of scalene Triangles:
acute scalene triangle:
An ACUTE scalene(all angles are acute) triangle contains three acute angles (each angle of an acute triangle is less than 90 degrees).sum of the angles of a triangle is always 180 degrees.An acute triangle may be isosceles,scalene or equilateral.

obtuse scalene triangle:
Obtuse scalene triangles have one angle that is greater than 90° degrees.(Obtuse triangles have one obtuse angle).sum of the angles of a triangle is always 180 degrees.An obtuse triangle may be scalene or isosceles.

right scalene triangle:
The right scalene triangle has one 90 degree angle and two acute (< 90 degree) angles.sum of the angles of a triangle is always 180 degrees.A right triangle may be scalene or isosceles.

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