In this work, a wideband Sierpinski gasket patterned equilateral triangular Dielectric Resonator Antenna (DRA) operating in the X–Band is proposed. This DRA is realised using Teflon. Its resonance and radiation characteristics are discussed. The resonance characteristics of Sierpinski gasket triangular DRA of first iteration and second iteration are reported that show an improvement in impedance bandwidth. An impedance bandwidth of 40% is obtained covering the entire X–band with similar radiation pattern throughout the band. The average peak gain within the band is about 6.5 dBi.