Shape Builder Sandbox

Pre-Algebra · Axiom Academy

Build a polygon, and its number of sides hands you everything else — the angles, the angle sum, even whether it counts as regular. Every polygon is just triangles in disguise A polygon is any flat shape with straight sides that close up — a triangle, a square, a stop-sign octagon. You don't have to memorize a separate fact for each one. Once you know how many sides it has, every other property falls out, and it all traces back to the one shape we already understand: the triangle. Watch a pentagon get sliced into triangles from a single corner. Three triangles fit inside, and since a triangle's angles always add to , the pentagon's corner angles must total . The same trick works for any polygon. Cut a polygon into triangles from one corner and you always get n-2 of them — so the corner angles add to . Add sides, and the angle sum grows Slide to change how many sides the shape has. Every side you add drops in one more triangle, so the angle sum climbs by another each time. The readout tracks the count of sides, the triangles inside, the total angle sum, and what each corner angle measures when the shape is regular. The angle sum follows one rule for every polygon: . Divide it evenly and you get each angle of a regular shape.

This is the written version of the interactive lesson above. See the full Pre-Algebra course.