Polygon Area
Half the absolute sum of cross products of consecutive vertices, the shoelace formula.
Decision · step 2 of 7Plane Geometry: Shoelace area of a pentagon
Edge AB: 1 x 2 - 7 x 1 = -5. Running sum -5.
What you will see
Triangles fan out from the origin, adding and subtracting area.
Cost
| Best | O(n) |
|---|---|
| Average | O(n) |
| Worst | O(n) |
| Space | O(1) |
How you work with it here
play it through, step one change at a time, scrub to any step, run it on your own input, try operations in any order.
Screen readers: Points announce coordinates and role; each step announces the geometric test and its result in words (left turn, intersects).
Reduced motion: Shapes appear in place; the sweep line jumps between events.
Before this
Taught by the same lesson
Plane Geometry covers these too, in the same run.