The Meaning Of Three Triangles

  • The three types of triangles can be characterized as equilateral, isosceles, and scalene by their lengths of the sides and the measure of the angles.
  • An equilateral triangle is a triangle with same side lengths and same angles.
  • The triangles with two equal sides and angles is called as an Isosceles triangle.
  • If all the sides and angles are different in a triangle, it is called as scalene triangles.

 

Meaning of three triangles:

 

                                 The three triangles meaning and they are given as follows,

 Equilateral triangle:

                          An Equilateral triangle is a triangle where all the three sides are equal in length.

                                                               

                   Area of an equilateral triangle = s2`4/3` square units

             Perimeter of equilateral triangle = 3s units

Isosceles triangle:

                          An Isosceles triangle is a triangle where two sides are equal and one side is different.

                                        

 

          Area of an isosceles triangle =`1/2`  b x h

             Perimeter of isosceles triangle = 2 (slant height) x base  units

Scalene triangle:

                      A scalene triangle is a triangle where all the three sides are different in length.

                             

 

            Area of a scalene triangle  = √s(s-a)(s-b)(s-c)

                                     Where, s =  `(a + b + c)/2`

 

Problems for the meaning of three triangles:

 

Example 1:

                   Find the area and perimeter  of a meaning equilateral triangle whose side length is equal to 6 centimeter.

Solution:

                               Area of an equilateral triangle = s2 `sqrt(3/4)` square centimeter

                                                                       = 62`(sqrt3/4)`

                                                                       = 36 × 1.732/4

                                                                       = 15.58 square centimeter

                         Perimeter of equilateral triangle = 3s

                                                                      = 3 × 6

                                                                      = 18 centimeter

 

Example 2:

               What is the area and perimeter of the triangle shown in the given figure ?

 

                         Area of the given triangle = `(1)/(2)` bh square units

                         Here, b = 9 and h = 4

                         Area =`(1)/(2)` × 9 × 4

                                 = 9 × 2

                                 = 18 square inches

                 To find the perimeter of this triangle, we need the slant height.

                 In the given diagram, the slant height of the triangle can be found using Pythagoras theorem

                 s2 = 42 + 32

                 s2 = 16 + 9

                 s2 = 25

                  s = 5 inch

                          So the perimeter of this triangle = 2s × b

                                                                        =  2 × 5 × 9

                                                                        = 90 inches

Example 3:

                    Find the area and perimeter of a triangle with side lengths 2 ft, 4 ft, and 8 ft.

Solution:

                        The given dimensions represents a scalene triangle

                   so, the area of a scalene triangle =`sqrt(s(s-a)(s-b)(s-c))`

                   To find s,

                    s =`(a+b+c)/(2)`

                  Here, a = 2 ft, b = 4 ft, c = 8 ft. 

                  s = 2+4+8/2

                     =14/2

                  s =7

             area =`sqrt(7(7-2)(7-4)(7-8))`

 

                     =`sqrt(105/2)` =10.3ft2

 

                  Perimeter of the triangle = 2 + 4 + 8

                                                      = 14 ft