We investigate the Fraunhofer diffraction of a Laguerre-Gaussian (LG) beam incident on a dynamic superposed dual-triangular aperture. The evolution of the diffraction pattern from this aperture is analyzed experimentally and theoretically. A special aperture, called the hex-star triangular aperture, demonstrates interesting diffraction patterns. Further, the diffraction properties of integer, half-integer, and fractional orders of topological charges at the Fraunhofer zone are studied by using the hex-star triangular aperture. This study can provide additional information to enhance the understanding of the diffraction properties of the LG beam transmitted through a complex aperture.