Which type of tool features a cross-shaped head to engage and tighten fasteners?

The tool that features a cross-shaped head designed to engage and tighten fasteners is the Phillips screwdriver. This design allows for better grip and torque when turning screws, which is especially beneficial for applications where greater force is needed without slipping. The cross shape of the head fits snugly into the corresponding recess of a Phillips screw, enabling effective engagement and reducing the likelihood of stripping the screw head.

In contrast, a flathead screwdriver has a flat blade that fits into the single slot of a flathead screw, but it does not provide the same level of grip as the cross design of the Phillips. A socket wrench is utilized with sockets to turn nuts and bolts and does not have a cross-shaped head. The hex key, also known as an Allen wrench, has a hexagonal shape that fits into the corresponding recess of hex screws, which differs from the design of the Phillips screwdriver. Thus, the features and design of the Phillips screwdriver make it the correct choice for engaging and tightening fasteners with a cross-shaped head.