One side of an equilateral triangle is 18cm. The midpoint of itsits sides are joined to form another triangle whose mid point, in turn are joined to form another triangle. The process is continued indefinitely. Find the sum if the perimeters of all the triangle and Ares if all the triangle?



By joining the sides of the equilateral triangle we get another equilateral triangle of side 9 cm. By doing this again and again the sides of the triangle will form a GP with a=18 and r=1/2

So the perimeter of all triangles will be= 3( the sum of GP)
=108 cm
I am trying.....
The area of the triangle formed will be 1/4 of the former triangle so the areas will again form a GP with a=81√3 and r=1/4