task(H5): polygon area calculation - shoelace polygonArea, formatArea with quadratic scaling, measure-area tool, properties panel area display

frontend/src/utils/format.ts

@@ -92,3 +92,28 @@ export function formatInputValue(
       return `${(mm / 1000).toFixed(3)}`;
   }
 }
+
+/**
+ * Format a raw world-unit squared area value (Task H5).
+ * @param rawSquared squared world-units (e.g. polygonArea result)
+ * @param unit target display unit
+ * @param scaleFactor world-units → mm conversion (like formatDistance)
+ * @returns formatted string like "5000 mm²", "50.0 cm²", "5.00 m²"
+ */
+export function formatArea(
+  rawSquared: number,
+  unit: UnitType,
+  scaleFactor: number = 1,
+): string {
+  const mmSquared = rawSquared * scaleFactor * scaleFactor;
+  switch (unit) {
+    case 'mm':
+      return `${mmSquared.toFixed(0)} mm²`;
+    case 'cm':
+      return `${(mmSquared / 100).toFixed(1)} cm²`;
+    case 'm':
+      return `${(mmSquared / 1000000).toFixed(2)} m²`;
+    default:
+      return `${mmSquared.toFixed(0)} mm²`;
+  }
+}