The present article explores the effects of moving lid on the forced convection flow of micropolar fluid inside a right-angle triangular cavity saturated with porous medium. The base and hypotenuse or inclined sides of the cavity are maintained at constant temperatures, while the vertical side of the enclosure is adiabatic and moving with constant velocity in upward or downward direction. The flow equations are simulated by using the robust finite element numerical technique. The pressure term from the momentum equations is eliminated by using the penalty parameter. For a consistent solution, the value of the penalty parameter is selected as 107. The simulations are performed for the cases based on the direction of moving lid. The numerical outcomes are shown in terms of streamlines, temperature contours, and local and average Nusselt numbers for sundry parameters, such as micropolar parameter, Reynolds number, Richardson number, Darcy number, Hartmann number, and Prandtl number. It is observed that the shape of the inner circulating cell is elliptic when the lid is moving in the upward direction and fluid is clear (Newtonian fluid). It is also found that average Nusselt number in both cases increases with increasing Prandtl number, Richardson number, micropolar parameter, and Darcy number, whereas it decreases with increasing Hartmann number. Further, it achieves a maximum when the lid is moving in the downward direction, regardless of the choice of involved parameters. The numerical code is also validated with previous published results. The investigation of the current study is beneficial in porous heat exchangers, construction of triangular-shaped solar collectors, rigid crystal, polymeric fluid transport, etc.