Oksana Mandrazhy, Amazing Properties of Fractal Figures, IJPMS Volume 16, International Journal of Pure Mathematical Sciences (Volume 16) https://www.scipress.com/IJPMS.16.37 Abstract: This article describes the process of research of the properties of geometric fractals by high school students. The general formulas of calculating the length and the area of the Sierpinski carpet have been derived in the article. The total surface area and the volume of the Menger sponge have been calculated in the paper. The amazing facts of geometric fractals have been revealed. For instance, if <i>n</i>→∞, the length of the Sierpinski carpet is <i>L<sub>n</sub></i>→∞, and its area is <i>S<sub>n</sub>→0</i>, similarly, if <i>n</i>→∞, the total surface area of the Menger sponge is <i>S<sub>ts</sub><sub>(n)</sub></i>→∞, and its volume is <i>V<sub>n</sub>→0</i>. Keywords: Geometric Fractals, Menger Sponge, Properties of the Sierpinski Carpet, Students' Research Activity