Area of regular polygons and composite figures

The area of a regular polygon is one half times its apothem times its perimeter, A = (1/2)ap, where the apothem is the distance from the center to the midpoint of a side. A regular hexagon with sides of 6 has a perimeter of 36 and an apothem of 3 times the square root of 3 (about 5.2), so its area is (1/2)(3 times the square root of 3)(36) = 54 times the square root of 3, about 93.5 square units. A composite figure is made of simpler shapes, so you find its area by splitting it into pieces whose formulas you know and adding, or subtracting for any holes or cut-outs: triangles (1/2 x base x height), parallelograms (base x height), trapezoids (1/2 x (base1 + base2) x height), kites (1/2 x d1 x d2, using the diagonals), and sectors of circles ((angle/360) x pi x r^2). Area is always measured in square units.

This explanation is AI-generated and can occasionally be wrong. 🚩 Report