The phrase "a path across the" is correct and usable in written English.
It can be used when describing a route or way that traverses a particular area or landscape.
Example: "We found a path across the meadow that led us to the river."
Alternatives: "a trail through the" or "a route across the".
A zigzag of gold material serves as a path across the stage.
Smoke billowed into the atmosphere and traveled eastward, cutting a path across the Midwest.
I was stretched in a thermal bath even as Syrian refugees struggled to find a path across the border at Zakay.
Carlton, 49, said his only paid work comes from seasonal jobs, the latest building a path across the tundra for hunting moose.
Two young men, John Rogers and William Lewis Manly, found a path across the Panamints, then returned with supplies to rescue the party.
Frank, nel mezzo del cammin, has great difficulty laying a path across the front garden ("Are you hitting rock again, Daddy?").
The pendant projects a map showing a path across a desert on Vulcan called "The Forge", which Archer believes will lead them to both T'Pau and T'Pol's mother.
Landing late the next day, he hired a small boat to take him to Caprera, then walked more than a mile on a narrow path across the rocky, windswept island.
The initial lighting reveals just a diagonal path across the stage; a second section shows the opposite diagonal, and the finale shows the routes crossing.
From the percolation theory, a rapid increase in electrical conductivity occurs when the conductive fillers form a conductive path across the polymer matrix of a composite.
A no man's land perhaps 200 feet wide of blasted-out buildings and overgrown bush, it snakes a jagged path across the city, separating a small, besieged enclave controlled by the government from thousands of radical Islamist insurgents.
