Calculations. Metric relationships in polygons

Metric relationships in polygons involve formulas for perimeters, areas, and sometimes diagonals, based on the lengths of sides and, in regular polygons, the number of sides and the apothem.

Important properties

• Perimeter of an n-sided polygon: sum of all side lengths.

• Area of a rectangle: $A = ab$ (where $a$ and $b$ are side lengths).

• Area of a regular polygon: $A = \frac{1}{2} \times \text{perimeter} \times \text{apothem}$.

• Number of diagonals in an n-gon: $\frac{n(n-3)}{2}$.

• Sum of interior angles: $(n-2) \times 180^\circ$.