Designs of a polygon shape microstrip antenna for increasing number of side lengths are studied. A detailed analysis is presented for the variations observed in the first and second order mode resonance frequencies in a polygon shape patch, from triangle to square to pentagon, ending up in a circle. Among all the polygon shapes, close spacing between the first two frequencies is obtained in the pentagon shape patch. A design of a pentagon shape microstrip antenna with a pair of slots is proposed. It gives impedance bandwidth of more than 700 MHz (> 55%), which is maximum amongst all the polygon shapes employing a pair of rectangular slots. The proposed design offers a peak broadside gain of 9 dBi over the bandwidth. A resonant length formulation and subsequent design methodology for the pentagon shape patch and its slot loaded variation are presented. This helps in the redesigning of a similar configuration in a given frequency range, using proximity and coaxial feeds.