A side of an equilateral triangle is 10 cm. The midpoints of its sides are joined to form an inscribed equilateral triangle, and this process is continued. Find the sum of the areas of the triangles of the process is continued without end.
Equilateral triangle is a triangle in which all its sides are equal.
Given: side = 10 cm
Area of an equilateral triangle = √3/4 a²
1st: a = 10 ; A = 43.3 cm² 2nd: a = 5 ; A = 10.83 cm² 3rd: a = 2.5 ; A = 2.71 cm² 4th: a = 1.25 ; A = 0.68 cm² 5th: a = 0.625 ; A = 0.17 cm² 6th: a = 0.3125; A = 0.042 cm² 7th: a = 0.15625; A = 0.011.cm²
Summation: a1/1 -r ; a1 = 43.30 ; r = 0.25
43.30 / 1 - 0.25 = 43.30/0.75 = 57.73 cm²
The sum of the areas of the triangles if the process is continued without end is 57.73 cm²
