Question

In an equilateral triangle another equlateral triangle is drawn inside joining the mid point of the side of given equilateral triangle and process up to continue 7times what is the ratio of area of fourth triangle to that of seventh triangle

Answer 1

Each new triangle has 1/4 the area of the previous triangle.
the ratio of the 4th triangle to the 7th is:
$(\frac{1}{4})^{4} : (\frac{1}{4})^{7} = 1 : (\frac{1}{4})^{3} = \boxed{64}:1$