One side of an equilateral triangle is 18cm. the mid points of its sides are joined to form another triangle whose mid points,in turn , are joined to form another triangle . the process is continued indefinitely . find the sum of the (1) perimeters of all the triangles (2)area of all the triangles

it is impossible because of infinite triangles


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
1 5 1
i couldn't help you with the area. I hope the perimeter helps.