house
廈 centers on a large, roofed building: a house or mansion. It conveys the idea of a substantial dwelling.
廈 combines 广 (building with a roof) and 夏, which likely contributes the sound. The character originally referred to a large house or mansion.
Under a broad roof 广, the inner part 夏 suggests summer. Imagine a spacious summer house—a grand mansion where you can escape the heat.
For カ, picture a car parked in front of a large house: car -> カ, and the house is so big it has its own garage.