By Richard Morgan • Updated Aug 30, 2022
Polygons—geometric figures formed by straight sides—come in many varieties, from simple triangles to complex star shapes. Common classifications include convex, concave, and regular polygons. A regular pentagon, for instance, is automatically convex because all its interior angles are equal and less than 180°.
Derived from the Greek word penta meaning “five,” a pentagon has five straight edges. In a regular pentagon, all sides and interior angles are equal, each measuring 108°. To compute the area of a regular pentagon, divide it into five congruent isosceles triangles. Calculate the area of one triangle and multiply by five. For example, if a single triangle covers 2.1 sq in, the entire pentagon occupies 10.5 sq in.
With the Greek prefix hexa meaning “six,” a hexagon consists of six sides. A regular hexagon’s six angles each equal 120°. Its area can be found by partitioning it into six congruent equilateral triangles. Multiplying the area of one triangle by six gives the full area. If one triangle is 2.1 sq in, the hexagon measures 12.6 sq in.
The Greek term okto denotes “eight,” and an octagon has eight sides. In a regular octagon, every side is equal and each interior angle measures 135°. By slicing the shape into eight congruent isosceles triangles, you can determine its area. Using the same example, an octagon with each triangle at 2.1 sq in totals 16.8 sq in.
Polygons are everywhere. The U.S. Department of Defense headquarters, famously called “The Pentagon,” is a large, regular pentagonal building. Bees construct hexagonal cells in honeycombs to maximize storage and structural efficiency. Architects frequently employ octagonal designs for gazebos and other structures. The ubiquitous stop sign in the United States is an eight‑sided octagon that signals drivers to halt.
