The person radical caps the character as a peaked canopy - a pictograph of the open umbrella seen from the side. Xinhua indexes 伞 under 人, and the cap is the most visually transparent part: the canopy spreading over what stands beneath.
The lower four strokes picture the ribs and central shaft of the umbrella beneath the canopy. They have fused into a non-decomposable bundle in the simplified form (from traditional 傘 which had four 人 figures hanging below the canopy) - the parasol body in skeletal outline.
