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This study aims to determine and describe students mathematical problem solving abilities in geometry material, namely to build a flat side space. Based on the results of the TIMSS and PISA studies and literature studies indicate that there are still many students who have difficulty in the cognitive process to understand problems and solve problems in word problems. This fact raises this research which aims to investigate the ability to solve problems and difficulties carried out by students in solving material problems in building flat side spaces. This research is qualitative research, involving 26 one of the junior high schools in Bandung which was selected using random sampling techniques. Analysis of the ability to solve problems in this study is based on Polyas steps, namely understanding the problem, devising the plan, implementing the plan and looking back. Data collection techniques used in this study were written tests and interviews. Data were analyzed descriptively. The results of this study indicate that there is a relationship between students problem solving abilities with reflective and impulsive cognitive styles. The results of this study indicate that Impulsive students tend not to go through the stages of planning completion, error calculations, and reluctant to re-examine the solutions that have been found. Unlike the case with Reflective students.