When it comes to describing an area that is unable to support life or vegetation due to various reasons, a few terms can be used as synonyms for "infertile area". Barren, desolate, arid, and wasteland are some of the most commonly used words. A barren land is typically devoid of any vegetation or animal life. Desolate, on the other hand, refers to a place that is uninhabited or left abandoned. Arid implies an area that is dry, lacking moisture and is unable to support plant life. Lastly, wasteland describes a land that is considered unusable, typically due to environmental damage or chemical pollution. These synonyms can all be used interchangeably depending on the context and are useful for accurately conveying the message.