Problems on the sum of the areas of infinitely many decreasing basic planar shapes

This contribution deals with the calculations of the sums of the areas of infinitely many uniformly decreasing basic planar shapes.Using the formula for the sum of an infinite geometric series, the formulas for the sums of the areas enclosed by an equilateral, isosceles and right triangle, for a square, rectangle, regular hexagon, regular octagon, regular -sided polygon, circle and ellipse are derived.Computer algebra system Maple was used for numerical calculations.