Step 1: Localise Area B to the lateral part of the back of the hand, the zone classically tested for radial sensory function.
Step 2: Trace the supply. The superficial branch of the radial nerve is the sensory continuation that fans out over the lateral dorsum of the hand.
Step 3: Add the digital detail. It covers the dorsal skin over the proximal thumb, index finger, and the lateral half of the middle finger up to the level of the proximal phalanges.
Step 4: Rule out neighbours. The ulnar nerve owns the medial dorsum, the median nerve owns the volar fingertips, and the posterior interosseous nerve carries no cutaneous sensation of this region.
$Area\ B = lateral\ dorsum \rightarrow superficial\ radial\ nerve$
\[\boxed{Radial\ nerve}\]